Just because you called it Mario Kart X I'll have to vote for 3D Mario instead (but I think Mario Kart is most likely)

Mario Kart 8 Omega Deluxe.
Zelda port. (maybe both combined?)
MP4

A tech demo game, Mario Kart 9, Metroid Prime 4, some older IP as a surprise, maybe a 3D Mario and/or Pokemon

I say maybe a 3D Mario as I'm not sure how big the team overlap are with 2D Mario. Since Super Mario Wonder just released, a 3D Mario title might not be feasible in time for the release if there's too much overlap.

Pokemon tend to come only after a console established itself a bit, so I don't think it will be a release title. However, considering the technical difficulties with the previous iterations on the Switch, they might be more willing to move to a new platform quickly this time around.

As for why no Zelda, that's because the IP will celebrate 40 years in 2026, and I'm sure Nintendo wants to release something big for the celebration, like how they wanted to do with Breath of the Wild for it's 30th birthday (which had to be pushed back due to the Switch releasing too late to fit for the celebration)

I’m going with March 25 launch headlining with Mario Kart World (what they will call it as it will have a huge open world esque online hub area not unlike Forza Horizon games) and MP4 exclusive for the Switch 2 to show off the full power of the system at launch. Probably a new Mario Party for the “party casual” game they always like to have. This is a decent parallel to what they did with MK8D/BotW/ 1-2 Switch for Switch launch. And just like that, 3D Mario will be the big first holiday title.

My prediction is a September 2024 launch with 3D Mario on day one and Metroid Prime 4 (dual release) in November. But I do believe that Nintendo will have another game available that isn't Mario Kart, Pokemon or Zelda. Personally, I think Kart is launching during the Apr/May/Jun quarter of 2025, with some kind of Pokemon title that November. I'm still wishing for that Ocarina of Time remake somewhere in there too, and hopefully, a brand new Zelda game in 2026 for the 40th anniversary (40th? damn, I'm old).

I can see them announcing a new version of Smash Ultimate.

I'll post my predictions for the first year:

3D Mario
I think 3D Mario makes the most sense as a launch title. They'll want a big IP for launch and a new Zelda game is still a few years away. Probably open world, something that will make a splash and sell consoles.

Mario Kart 9
Mario Kart has almost always been one of the early titles for Nintendo's systems. With the franchise being bigger than ever, I think they'll want to make sure Mario Kart will be on the new system in the first year.

Something Zelda
Obviously, Zelda is a huge franchise for Nintendo. I think there'll be something Zelda related in the first 12 months: That could be a BotW + TotK remake bundle to show off the power of the new system (60fps, running at 1440p or 4k resolution, higher draw distance, shorter loading times, etc.). It could also be a Zelda collection consisting of Wind Waker 4K, Twilight Princes 4K and Skyward Sword 4K (or the N64 titles). Or maybe a fully-fledged remake of Ocarina of Time, made from the ground up.

Smash Bros. Ultimate Deluxe
With Smash Ultimate being hard to follow up, maybe Nintendo will want to remake the game: 4K, maybe 120fps, including all the previously released DLC and maybe a new fighter pack. They could remake some graphical details, add a few additional modes, etc. Ultimate is, well, pretty much the ultimate Smash game. And I think remaking it and waiting a few more years before releasing a true sequel would be a sound plan.

Metroid Prime 4
At this point, I think Prime 4 is a Switch 2 game. It also shouldn't take much longer for the game to be revealed. Expecting this to drop before the end of 2025.

I only did so because we will be on the 10th installment of Mario Kart in the series. And they've been numbering them recently, and no one uses 10 except microsoft, plus X feels more "future-related".

I'm not saying those are the names of the games, but I can make some educated guesses (they'll most likely be wrong).
What should the next Mario Kart be called?

The 2D Mario series is developed by EPD 10 (they are also in charge of developing Pikmin). Nintendo stated that they will "try not to let everyone wait" for Pikmin 5. Considering the gap between Pikmin 3 & Pikmin 4, 10 years, we can expect Pikmin 5 to release before 2033 (I'm guessing 2030). And yes we just got the new 2D mario with Wonder (I think they can do so much with the Wonder Seed idea, and remake old games with the wonder seed).

The 3D Mario Series is developed by EPD 8 (they've worked on flipnote studio, mario makers, and NES Remix). Their last full game was back in Nov 2013, and the Switch port was released in Feb 2021 with a new expansion Bowser's Fury. 

If you are saying Nintendo will come out swinging this hard on launch day, then that would be something wonderful.

Launch Day
3D Mario
New IP
First 6 Months

Super Smash Bros. Ultimate DX

Mario Kart

Metroid Prime 4

Third Party In The First 6 Months

Grand Theft Auto V

Red Dead Redemption 2

Final Fantasy VII Remake

Call of Duty