Yes.
Bubble literally consolidates the multiple searches into a single search fully delegated to the server?
Correct, the :merged with operator (at least in this context) merges the expressions into a single DB query.
Or, do you just mean that in practical terms what are literally 3 separate sequential searches yield the same result as if it were a single search?
Nope, I mean only single DB query will be made.
FWIW, my approach in this type of situation is typically:
Role is in Arbitrary text:split by ,, withAdmin,Gestionnaire,Enseignantin the Arbitrary text
That would work if your Role field is a single Text (although I wouldn’t recommend using Text for Role fields).
But, in your case the Role field is a list - hence why you can’t do it that way.