The first thing I notice here is the snap reference.
Remove ~/bin/exercism and do an uninstall for the snap installation of exercism.
Install the executable for Ubuntu instead, place it in a directory named ~/bin, ensure it has executable bit set, chmod +x ~/bin/exercism and restart the terminal, and you should be able to execute the exercism without any path reference needed (so no ~/bin/exercism as Ubuntu places this directory in the path if it exists.
Snap has been a problem, and hopefully we will be doing away with those instructions soon, as we are not maintaining this well. (I don’t want to blame Snap, it presumably is a fine system!)
Snap is not really supported in wsl. I know it got support in windows 11 for not too long ago (I have not got it to work on my windows 11 machine though) but I am unsure if it actually works on windows 10.
If you actually want I can jump into a call with you and help you step by step.(later today or whenever), since exercism doesn’t require snap. But snap with wsl isn’t a great combo unless you know exactly what you are doing (which I don’t).
If you use Ubuntu as your WSL flavor, then ~/bin is the preferred path.
Ubuntu will, if and when that path exists, place it in your path automatically. And so having the executable there, with a chmod +x ~/bin/exerism to give it that executable bit, should allow you to execute it in your terminal under a shell such as bash.