Sand is made of silicates holded together with strong chemical bonds. 99,99% inert, no it cannot leach silicates in the water. It would take decades, centuries. It's like saying your aquarium glass leach silicates since glass in made of silicates too. It's an Urban legend circulating on the internet.
Not long ago I would have agreed with that statement. Most sand and glass is made of silica. Silicates however are not silica And they can behave very differently.
Sand has a lot of silica in it and it may or may not have silicates. Silica is mainly SiO2. Silicates are SiO1, SiO3, SiO4 and there are other forms of silicates. Silica (SiO2) is inert and not soluble in water Silicates in comparison are reactive and will bond with metal. Many forms of Silicates are not soluble but some are. Sodium silicate for example is somewhat water water soluble. Silicates will support diatom growth. Silica will not.
IF you water is low in Silicates, any silicates in your sand should gradually get washed out over time with water changes. So a new tank
can have silicate and diatoms problems but over time the silicate levels should drop and eventually the diatoms should die off. However if the primary source is your tap the problem may not get better.
I did a search and apparently phosphate removers also remove silicates from the water. Unfortunately you don't want to remove phosphates from your fertilizer. You might want to set up a bucket or water (enough for a water change and then put in a small filter made for a small aquarium and put phsphate remover in the filter. Put the filter in the bucket By the time you are ready for your regular weekly water chang you should have phosphate, silicate free water to put into your tank. Then add your fertilizer. If it works your diatom growth should slow and may stop. It is also possible that silicates might be reacting with your micros in your fertilizer or somehow slowing the growth of your plants.
I was thinking the silica came from my tap water as well, because its GH is so high. But the tank has had the same kind of water for years and it used to run well without diatom.
utility water chemistry can change over time. In the past your water may have had low silicate levels but now it may have a lot more. you might want to look around . maybe you can find a silicate test kit. If so test the water first before trying a phosphate remover.
I personally have not had a silicate problem but it might explain your problem.
I looked through your other tread about your plant growth. You got good advice. That advice generally works for most people. But Have noticed a small number of people like you that still have problems. I am beginning to think that some of these problems might be nutrient overload or toxicity issue. This occurs when you have too much of one nutrient. And this nutrient make it very difficult for your plants to take in other nutrients. This like list some of the toxic symptoms.
To elements on that list have been a concern of mine. Copper and Zinc. These are often used in pipes to reduce corrosion. But in the process of doing that they can also dissolve in the water Recently I saw a water quality report that showed zinc levels at 0.35 ppm when you only need about 0.02ppm in a fertilizer. My tap water has 0.05ppm of copper in it. About 5 times more than needed. I never used tap water in my aquarium. I have always used RO water. But the fertilizers I tried all had very very low levels of zinc and copper and that made it very difficult for me to get good consistent growth.
I would try the the bucket with phosphate remover first. IF that doesn't work you may want to try softening your tap water by mixing it with RO water.