I am unclear what the issue you are seeking to address here is; what is wrong with your path?
Some command you’ve been given is not working?
Homebrew has already modified your path, based on what was showed. You’re also seemingly on a Mac minimwith Apple silicon.
Some background, comments:
The contents of the environment variable PATH is an ordered list of places to look for commands you enter, with zsh and most other shells separating each of those places with colons.
.NET is Microsoft focused. And the .NET RAPTOR directions I’ve found for installation are just, well, bad, so don’t you feel bad about the issues you’re having here.
zsh can read from various scripts at login, ~/.zshrc is but one.
Those scripts are ~/.zprofile , ~/.zshenv, ~/.zshr, and ~/.zlogin, and leaving ~/.zlogout for another time.
You can cat each of those files, if present. or nano, if you want to edit the file.
And to add stuff to the path in zsh, use (lowercase) path as follows to prepend or append the directory:
path+=('/path/to/wherever')
path=('/path/to/wherever' $path )