VS Code can have multiple formatting extensions for same language installed, but only one of them (selected by some magical "score") will be using for formatting by formatting key.
If this extension does not work:
Try to use it with command (F1 or Ctrl+Shift+P: perltidy).
Try to disable other perl formatting extensions.
Try to install perltidy binary from your OS repository.
1. Q: I'd like to use .perltidyrc specific to different projects.
A: Use "perltidy-more.profile" option and set it to ".../.perltidyrc". Three dots is perltidy specific option to indicates that the file should be searched for starting in the current directory and working upwards. This makes it easier to have multiple projects each with their own .perltidyrc in their root directories.
2. Q: I'd like to run perltidy in docker container.
A: Use shell script like this and set it as perltidy-more.executable in options
exec docker run --rm -i -v "$PWD":/app -w /app avastsoftware/perltidy $@