[FEATURE]: Support mise in desktop app

[nesl247]

Feature hasn't been suggested before.

• I have verified this feature I'm about to request hasn't been suggested before.

Describe the enhancement you want to request

My team uses mise (https://mise.jdx.dev/) to install tools like lefthook, etc. rather than having to include it via npm, composer, or even globally. This works fine when running opencode in the terminal, but when using the desktop app, none of the binaries are found because the $PATH isn't modified via the hook that mise uses in the shell.

It would be great if mise support could be added. In VSCode, IntelliJ, etc. there are plugins for this, but nothing here.

[github-actions]

This issue might be a duplicate of existing issues. Please check:

• PATH is not inherited from invoking shell #2202: PATH is not inherited from invoking shell
• Shell sessions losing $PATH value from parent shell #4968: Shell sessions losing $PATH value from parent shell

These issues describe the root cause of why mise binaries aren't found in the desktop app - the PATH environment variable isn't properly inherited from the parent shell. Adding mise support would likely be resolved by fixing the underlying PATH inheritance issue.

Feel free to ignore if your specific case requires additional consideration.