It’s IP vs. publishing rights. In an effort to attract third party devs I can see Nintendo being lenient on who owns the franchise in exchange for timed exclusivity.
I believe the Bayo IP is owned by Sega. They allow Nintendo to fund and publish the sequels (and re-publish/port the original.) That’s why no one thought Bayo 2 would ever happen – Sega was clearly completely uninterested in furthering the series, and in situations like that it pretty much ends with the publisher. Nintendo swooping in to fund a franchise they don’t even own is pretty unprecedented.
More baffling to me is Microsoft’s strategy of “yeah I guess even games that were developed by owned first party studios can get ported to competitors’ systems.”