I really agree with
@dw1305, corydoras need a minimum of 10 (in my experience, any less and they hide all the time and don't move much at all) to feel confident, and they also need lots of hiding places. Ember tetras are similar, they will be very shy if these needs aren't met which won't be enjoyable to watch. Really in a tank this size you should only keep one species at most.
The way you're thinking about stocking in terms of inches is considered a bit old fashioned as it can be misleading, it's now more about looking on places like seriouslyfish.com and aqadvisor.com and seeing what minimum tank size the fish you want need, how big a group they should be (some fish singles, some in big groups) as well as all their other needs/how they live in the wild and making sure your tank mimics what they have in the wild so they're as comfortable as possible. People on UKAPS also have a really good understanding of the needs of fish and can advise you with their real-life experiences on stocking. Some people don't mind keeping their fish in smaller tanks (or overstocking medium-sized tanks), and some people have more strict standards for keeping their fish (keep to a small number of species and give them as much space as possible + mimic their natural environment). No judgement either way, but personally I went from the first group in thinking about stocking (I wanted to keep every creature I liked in one tank) to the second group (I now keep a limited no. of small fish species in larger groups, in a larger tank) purely from experience - I have noticed the fish are significantly "happier" and exhibit lots of interesting natural behaviour when I apply those stricter standards, and I find that that is much more satisfying to watch and experience. There is much less anxiety in fishkeeping when I know all my fish's needs are met too.
I have noticed my fish are at their most confident when they're surrounded by big bushes of thriving real plants, big handfuls of dried leaves and dappled light from floating plants and hardscape. This makes sense because tiny fish like pygmy cories, ember tetras, etc, are so small, and thus everything in the wild finds them to be a delicious snack. They are naturally shy and need hiding places to escape into to feel safe enough to come out. Adding a few handfuls of leaves is super easy, will soften your water a bit, and just makes tanks look more natural in a beautiful way. I use oak, beech, catappa, walnut & my favourites right now are magnolia grandiflora if you have one of those in your area, they look beautifully tropical in a tank. I also suggest that you add a few more plants to the tank, I know you want to leave space for the plants you have now to grow but it will 100% make any animals you add happier now, and it's fun to try different plants. Another good option is some floating plants to dapple the light, animals really like that too, in the wild they have trees and plants dappling in the light and hiding them from predators. Floating plants grow very fast too, so you don't need much to start with.
