Marvel Spider-man isn’t First party because Sony published and developed it.
Lot of grey areas fellas (and ladies) there are quite a lot of nuances and not everything is the same + we have no insights in contracts.
-Sony leveraged their movie rights, don't own the full Spider-Man IP. And by the first SM Sony didn't own Insomniac.
-Then we get Koji Pro which is independent creating a Sony owned IP (after the bs of MS) using a first party engine.
-Shift Up where Sony doesn't own the IP but the studio signed a 2nd party contract for the game and no PS studios logo.
-Helldivers which is classic 2nd party, Sony owns the IP but not the studio.
-Square that makes the FF7-trilogy exclusive where Sony basically funds the project partially but owns nothing
-MLB that license the IP while made by 1st party
Marvel's Spider-Man, Death Stranding, Stellar Blade, Helldivers and MLB are a PS first party games because Sony, the platform holder published them.
The FF-trilogy are 3rd party games because they are published by Square Enix (a 3rd party company, which means not owned by the platform holdeR).
Doesn't matter who developed it or who owns the IP, or who made its game engine, or who has movie rights:
1st party game = published by the platform holder
3rd party game = published by a company not owned by the platform holder
This how it has been always, since many decades ago.
In the case of Death Stranding, outside the "1st vs 3rd party" talk, Sony is the owner of the IP, so who decides where the game can be released. Kojima asked to release it somewhere else and Sony allowed him to do with other publisher as an exception, because back then they didn't publish their tentpole console games in PC.