Each auth has it's own Guard in Laravel when you setup multi auth.
Then in spatie you need to specify which guard name you want to use for that role or permission you create or check. See https://spatie.be/docs/laravel-permission/v3/basic-usage/multiple-guards
It's more simple to have just one auth and multiple roles/permissions that manage, and most probably is enough.
There are some package that can help you build multi auth skeleton in case you want go with it, see: