I can understand maybe you're new to this and uncertain, but there really isn't a need to ask everything. Not when you can perform trial and error.
Just load up the mon in the SWSH save, and if it's legal, it's legal. No need to worry so much about it.
Tho, if it's pre-SWSH caught mons, not transferring via Bank would mean no proper transfer attached to the HOME ID generated on their end.
Presently, we don't know if that matters. Ultimately I've said what I've said.
It's not like we work for Gamefreak. All we know is whether stuff is legal or not, for the most stuff.
The rest is really your prerogative.