The question of who can survive on first party alone is a simple question with an obvious answer, because Nintendo has literally been doing it for generations. But you don’t like the answer so you are trying to harp on irrelevant semantics.
It’s not any of our fault that Microsoft or Sony don’t have stables of long standing high quality IPs that they can outsource to other studios to make first party games with. Nintendo on the other hand does. They also have a much stronger first party offering. This is obvious when you look at sales (nothing MS offers is close and now with GamePass nothing will ever be close, and the only Sony titles that approach Nintendo sales do so with massive bundling and deep price cuts).
But you know all of this which is why you want to exclude it, because excluding it means nothing to MicroSony but has a big effect on Nintendo. All of these companies consider these games first party, get with the times. It doesn’t matter what you think qualifies as first or third party, it’s widely accepted what is first party by pretty much everyone else.
Sony doesn’t have a Fire Emblem or Pokémon in their arsenal to outsource but if they did, you’d consider it first party.
What a stupid hill to die on.