fish, version 3.3.1
xterm-256color
Ubuntu 20.04.3 LTS
After #6001 completion registered via path work for relative directories: complete -p /home/user/myscript ... would work for ./mysript and for /home/user/myscript, but not for $HOME/myscript or ~/mysript.
In file completion variables are resolved. I think it's good idea to respect variables for custom completions.