So this question is more generic than prisma - it is also true when running updates/deletes in raw SQL.
When you have extra where clauses to check for ownership, it's difficult to infer which of the clause(s) caused that if the update does not happen, without further queries.
You can achieve this with row level security in postgres, but even that does not come out the box and involves custom configuration to throw specific exceptions when rows are not found due to row level security rules. See this answer for more detail.
I tend to think that doing customised stuff like this is rarely worth the tradeoff, unless you need specialised UX for an uncommon circumstance.
What I would suggest instead in this case is to keep it simple and just use extra queries to check for ownership, but optimise the UX optimistically for the case where the user does own the entity and keep that common and legitimate usecase to a single query.
That is, catch the exception from primsa (or the fact that the update returns 0 rows, or whatever it is in different cases), and only then run a specific select for ownership, to check if that was the reason the update failed.
This is a nice tradeoff because it keeps things simple, and only runs extra queries in the (usually) far less common failure case.
Even having said all that, the broader caveat as always is that probably the extra queries simply won't matter regardless! It's, in 99% of cases, probably best to just always run the extra ownership query upfront as a pattern to keep things as simple as possible, which is what you really want to optimise for over performance until you're running at significant scale.