When they launch depends on a number of things. Yes they have previously cut off sales of systems (GBA and DS) to launch a successor, but both of those times they were worried about the much more powerful Playstation portables perhaps stealing some of their market, which of course didn't really end up happening, but it spurred them to cut off two systems that were still selling well. That's not a problem right now, there is no handheld/hybird system coming out that Nintendo has to be worried about.
Presumably Nintendo has already architected the next gen and has the chips picked out and everything, and have sent dev kits to developers so that studios can be putting out games in 2025. And Nintendo of course has to start manufacturing the systems, including planning and setting up the facilities for that, which takes some time but not a super long time. And they probably want to at least have 3D Mario and MK9 ready for launch, but likely they've been working on both those games for numerous years now and could have those ready whenever they decide to launch the system. Really Nintendo probably just needs to make a firm decision on the launch period like 9 months out or something (granted I have no industry insider knowledge or experience here, but that time frame seems reasonable).
And they probably have a general time frame they are shooting for, which I think we could reasonably say is probably roughly mid-year 2024 to mid-year 2025. Nintendo can narrow down that range based on how Switch continues to sell. While the second half of last year and earlier this year it looked like Switch was finally starting to fade a bit, it seems TotK turned that around entirely and sales are much stronger than they should be following just a big game release. It sure seems like TotK (and perhaps the Mario movie as well) has brought about a resurgence of interest (in the form of new buyers) for the Switch. Switch looks totally different these past two months than it did the previous 12 months.
It sounds like Switch certainly has a 2024 lineup planned, but the one thing I would question is how much of a first party lineup do they have planned beyond say the next 12 months. They aren't gonna be starting up development on new Switch games at this point. So that is a limiting factor for extending the Switch's life, unless Nintendo is cool with just selling systems, third party games, and previously released first party games for a while and just letting Switch cruise. But more than likely, with how old Switch will be in a year, if they no longer have any first party game announcements people will stop buying the system as much and will be in wait mode for the next gen to launch.
Long way to say basically they're probably gonna go to Fall 2024 or sometime in the first half of 2025.
Even just a couple years ago lots of people were saying Nintendo needs a new system in 2022, and even just last year lots of people were saying Nintendo absolutely must have a new system in 2023. Obviously with Switch sales surging now in mid-2023 the idea of releasing a new system in the next 12 months seems pretty silly. For several years now 2024 has seemed the most likely year for next-gen, and it still did until the past couple months. If the strength of these sales continue, even just to the point of selling close to what they sold last year, 2025 definitely starts looking like a possibility.
Also, yeah, they haven't done any price cuts, and while Nintendo often doesn't do price cuts these days, they are gonna run into a problem when next gen hits of presumably the new system launching at around the OLED's price, or maybe at absolute most $50 more than that. If they expect to continue to sell Switch's in its post-life for a bit they better be planning to drop the OLED (and therefore presumbly the other models) a minimum of $50 before next-gen starts. And if they drop prices that also probably buys them a few months longer for Switch's life before they need to release the next system. But in the end, at some point they are just gonna have to pull the trigger because they are out of Switch games and have next gen games ready to release and waiting.