Hi, I'm new to the forums, but not to the hobby.
I personally wouldn't add anything else. I hear people advise against neon tetras for bettas as they are very fast and flashy, which may stress the betta out. It also depends on how aggressive your betta is. I've heard of people who would keep neons with their bettas and the betta would try to fight or even kill the tetras.
People commonly keep neons with bettas with no problems, so you could try it, but I would suggest getting a bigger tank like a 20g long first (if you can) so that all of the fish have more space. Neons are very active so even smaller schools need room to swim around.
The only other tankmates I would recommend for a 10g would be shrimp. Though your betta may or may not end up killing them.
Just my personal opinion. If anyone wants to add in, go ahead!
Best of luck.