there isn't a hook for executing shell source, but it would be possible to add I think. The current hooks already execute inside of a shell function so there would just need to be a way to declare that you want a hook to run inside the shell, maybe like this:
[hooks.enter]
shell = true
run = ". completions/mycli.sh"
I made an issue if you'd like to track: https://github.com/jdx/mise/issues/3412
Very helpful! If this can be made to work I may switch from direnv