I use Brightwell NeoNitro to supplement nitrate. I like using things made for the reef hobby because I know there won’t be weird contaminants in a future batch, and they come with clear instructions for reef use. And unless you starting using it by the gallon in the future there isn’t a significant cost difference. Lots of people use the DIY supplements successfully, I’m just stating my preference and what I’d suggest for someone just starting to dose something.
Feeding more will give you more phosphate as well as nitrate by the way. Depending on your target values you probably don’t want to keep boosting your phosphate levels higher. If you supplement nitrate without adding more phosphate, it will gradually bring the phosphate level down.
The reason why zero nitrates promotes Cyanobacteria is because they are one of the few organisms in our tanks that can fix N2 gas from the air into ammonia, which they then consume as an alternative to nitrate. This gives them an unfair advantage against other surface colonizers when nitrate is zero, since everything needs some form of fixated nitrogen to grow.