I'm gonna say Fall 2024 is most likely. I could see Spring 2025.
I'd say Spring 2024 is a possibility only if sales drop a bunch in 2023, but that doesn't seem too likely with BotW2, possible price cuts, and presumably plenty of other games getting ready for 2023.
2024 feels too soon for a new system but with Switch holidays starting to lose steam I'm guessing they'll want to have the successor out for 2024 holiday. And unless they start doing another round of some of their games on Switch it feels like they'll have plenty of games to get up to holiday 2024 but not beyond, at which point MK9, 3D Mario, Pokemon, etc should be ready with next-gen iterations.