same issue here but on the PC. the extent you can program with this bug in place is having a repeat command block set to always active. anything more advanced such as IF statments or anything to do with chain blocks is impossible. nothing works. however when tried on the PS4 and Nintendo Switch everything works perfectly. hopefuly this will be resolved in the 1.16.2 hotfix. until then if you want to program then try it on another device and turn it into a realm and then download it onto your other device. i've found that is the only way to make it work which is unfortunate.
I have found that on my laptop with a NVIDIA GTX 1050 there is a client side fix to the issue. this may not work for everyone based on their GPU.
to get to the file, follow these steps
1. go to %appdata%
2. Local
3. packages
4. Microsoft.MinecraftUWP_8wekyb3d8bbwe
5. LocalState
6. games
7. com.mojang
8. minecraftpe
9. Options.txt
change gfx_vsync:1 to gfx_vsync:0
ater changing this, save the file and boot up Minecraft. for me all problems are resolved after this no lag from keyboard or mouse. this may not and is probably not a fix for everyone and Mojang still needs to fix the issue. hope this helps.