You have great advice already. I'll give my 2 cents for what it is worth.
1)We often don't have enough nitrogen (nitrate) in our tanks if we are heavily planted. The photo you took a pic of is the nit
Ate test. The nitr
Ite test is blue. You don't want ammonia or nitr
Ite, but you want 10ppm+ of nitr
Ate. From here on out, I'll focus on nitr
Ate so I can stop typing it so funky haha
Turns out nitrogen is a macro that is crazy important for plant growth and most people overlook it for micro nutrients like in the "florish" bottle, or believe that nitrates are bad based on fish keeping articles read online. We are running planted tanks which require different care than a "fish tank". 0 nitrates in your water will certainly be the cause of stunted growth and Algae. I have 2 tanks that require weekly dosing of a nitrogen source in order to keep growing. With CO2, everything is sped up multiple times the speed of normal growth... The only way you would naturally supplement is to add multiple times the fish you would normally have to compensate for the sped up plant growth... which isn't realistic in most cases. I would caution against over feeding for more nitrates just due to the fact you are adding nitrate and phosphate, but missing all the other micro nutrients. plus it is tough to measure out "how much is too much or too little" for your tank. Also consider it may hurt your fish by over eating (depending on the species).
2)After getting sucked into the Seachem lineup buying individual micro and macro nutrients to dose and trying to dose when it is needed, I realized it was WAY easier and cheaper to do an all-in-one water column fertilizer and change out the water according to the directions (EI method). Turns out I'm not a scientist specialized in locating the difference between dark green veins and a light green leaf... and then plugging those observations into different plant species? Forget it. I recently switched to the EI method (dosing more macro and micro nutrients, and then removing out of the water column later with water change), and am much happier than I was pulling out my hair trying to figure out what plant deficiency there is. With CO2, you almost certainly want to do the EI method instead of individually adding stuff... Things change quick in Co2 tanks, and by the time you found out what you were missing, and how much you need, you could have already had a massive algae bloom or plants dropping leaves/yellowing/dying off.
3) This was touched on already, but it's really important to know what plants you have. Group them in two fertilization categories: #1: Water Column Feeders #2: Root feeders. Aquasoil is great for your root feeders, but it will eventually exhaust itself as mentioned (after around 10 months-1 year). That is partly why I use sand blasting sand. I'm going to have to put root tabs in the substrate anyways, so why not just do it now and save the few hundred dollars? Anyways, you'll need root tabs for your root feeders, and liquid ferts for your water column feeders. Most tanks have both categories, so you'll have to fertilize both ways.
4) Even though carbon (Co2) is a macro nutrient, you probably don't need it. However, expect slower plant growth if you do without it. That's really the only benefit to Co2 other than maybe coloring of specific species. Most plants in nature don't require higher than normal water Co2 levels naturally (makes sense, right?). The biggest downside of Co2 is the sped up plant growth will cause more dramatic algae blooms/dropping leaves/yellowing/dying off if you miss something. And due to the sped up growth, you're going to exhaust nutrients faster than if you were just dosing fertilizers without Co2. I think Aquarium Coop actually did a video on this explaining it better than what I did above, but that's the crash course summary. Tread lightly with Co2. If your tank is out of wack, make sure you have a great balance of nutrient and light before using Co2 in higher doses. Think of Co2 as adding a performance modification to a car. Don't try to slap a turbocharger on your car that is not tuned to perfection for the addition. Otherwise be prepared for engine knock and a dead engine. (bad analogy unless you're familiar with cars I'll admit, and probably a bad comparison anyways. haha)
5) Once your ferts are dialed in perfectly, remember plants take time to grow. Months/years to fill in. The tanks you see on this forum are not created overnight. Planted tanks take extreme patience. Get excited when you see a new leaf from one of your plants. that means you're doing something right! We are all impatient. Keep in mind, carpets take way longer to cultivate than just growing plants in an aquarium. Unlike your stems and rooters, I'm guessing you're waiting for your carpet to not only thicken, but spread too... or propagate. That is a whole extra step in growth you are expecting out of your carpet that you aren't expecting out of your other plants. That is the "slower" part. However, judging by your post, it sounds like everything is somewhat stunted (nutrient deficiency). But still a good thing to remember when you get your nutrients corrected.
Other members nailed it on the head. It is likely nutrients for nitrate. But if you bring those up, be prepared for other macro and micro nutrients to be exhausted with your Co2. That is why I suggest the EI method of dosing (and have a schedule as mentioned too by the previous poster). It takes the guess work out of what you need, why, and how.
Not wanting to change water and skipping the El method while running CO2? That's going to be tough. As hinted above, Co2 is a demanding tank maintenance wise, and you have to be super on point/dedicated. With the sped up growth, it is going to need quite a bit more attention compared to even a tank with ferts without co2. You have way less time to react to a deficiency with the Co2 speeding everything up than if you were just watching the plants grow more naturally with fertilizers. And that is how people's tanks on here sadly go from being amazingly beautiful, to an overgrown algae mess and melting down seemingly in no time.
Overdosing (EI method) prevents anything like that from happening accidentally. And quite frankly, since even trying to calculate out deficiency corrections with no measurements on most macro/micro nutrients, we have basically been doing a version of EI method anyways for ages as far as I'm concerned.
I know you are trying to shy away from dosing more ferts in the tank than the tank needs (EI method). The fact is most nutrients we can't test for anyways in water, so to a degree, we are all "overdosing" our tanks to a degree, and just estimating how slim we can be with our dosing with no means of measuring. Or on the contrary, others wait to identify a deficiency, and then guess to see how much is needed to get the deficiency to go away. That can be a real challenge and exhausting to manage especially since you can't see results quickly. That's why most EI dose especially with a Co2 tank that exhausts resources quickly.
Also keep in mind, all-in-one fertilizers could actually help with your nitrogen deficiency as well. Consider something nitrogen heavy if you are low on nitrates at the end of each week like Thrive. If high in nitrates due to fish or feeding, consider an all-in-once fertilizer that is low in nitrogen. EI dosing will allow plants to out perform the algae and problem solved! Then patience with the carpet. Keep the Co2 running if you already have it

might as well use it if you have it! It is true that no ferts should be adding to your ammonia or nitr
Ite level. Either the tank wasn't cycled, or your dramatically increased the number of fish in your tank, and your Nitr
Ate factory had to catch up. Changing too much water can cause this problem too creating what we refer to as a "mini-cycle".
Finally, after nutrient is addressed, consider taking a look at your lighting to address your slow growing carpet (keep in mind it sounds like yours is totally stalled due to algae and no new growth). Carpets usually require pretty strong lighting, but nothing crazy like 10 hours of lighting. While the light you have is a great fixture, consider placement and intensity at the depth of a 55 gallon. Also consider the amount of time the light is on.
In my experience, 8 hours+ gets iffy with growing algae no mater the light intensity. I think most of us are around the 8 hour photo period. I run 8 hours with a 1 hour ramp up and 1 hour ramp down. That's a total of 10 hours, but likely more like 8.5 hours of usable, good light for the plants. I also wouldn't use the 24/7 mode for various reasons.
Carpets need some really strong high light. and I'm not sure a single 48" fixture is enough if you're trying to get high light at the bottom of a 55 gallon. That tank is pretty deep. But definitely ask in the forums after you cut back lighting to 8 hours, or even 6 hours temporarily while you get your algae under control, and after you figure out your nutrients.
While I'm not familiar with 55 gallons specifically, I did need 2 Fluval 3.0s for my 40 gallon breeder (the breeder is shallower, but wider...). The depth of the breeder is kind of a sweet spot for plants because it is the maximum depth you can really go to get some strong PAR under 1 fixture, but you need two for the light spread from front to back of the tank. I think the 55 gallon is a fair amount deeper than the 40 gallon, and with 1 fixture, it might not be enough par to really get to your carpet as a high light especially if your one fixture is in the middle or towards the back of the tank. PAR degrades not only with depth, but distance off center as well from where the light source is. So you might be high light directly under center of the fixture, but substantially weaker up at the front of the tank. Carpet up front and fixture in middle might yield a weaker PAR reading than you would think.
you might need to research what others have done to get "high light" in a 55g in carpet situations as the 40g breeder is a little bit of a different animal, but the same logic for depth and spread apply to your 55g.
I will say, algae is not due to dimmer lighting almost ever... slow growth is due to lighting mostly (depending on species). algae is almost always nutrients missing. Too long of light will cause algae too. This is unlikely your culprit if your lighting is on 8 hours or less and your running that one lamp at full blast. The key is your carpet will still grow in with even lower than optimal light intensity, but it may not propagate how you want it to, and will be super slow growing with the dimmer light setup. But like I said, check in to see what others have AFTER you fix your nutrients. The nutrients on the other hand is definitely an issue and easily correctable as well.
Feel free to message me if you need any help!
Edit: Just saw you moved your fixture over your carpet during the day. This is a good move, but they're still going to show those symptoms until you fix the nutrients missing first

Do you know the par at the depth of your lamp to the substrate for that fixture by chance? A 55 gallon is pretty deep! It might grow your stems and rooters fine that have some height, but a foreground might not have enough light getting to it to really thrive after your nutrients are addressed. I don't know the PAR numbers though for that tank depth.