What will Nintendo do with the next Smash Bros??

This intrigues me to no end.

They literally did the 'Ultimate' version of what Smash has been building toward since Melee. What now?

It is hard to imagine just another typical Smash. I would probably not even bother with it and just keep playing Ultimate on the next-gen (assuming backwards compatibility because Nintendo execs would need to be locked up in a mental hospital if they didn't do backwards compatibility).

But Smash is so popular it is also dangerous to mess with the formula.

The only thing I can think of is to just make it a free game on NSO Expansion Pack and just keep building on it over time, to entice more people to get NSO. Putting their ultimate competitive online game on their online service to push sales of that service to be a more premier service definitely makes sense if they want to start taking online seriously. Then they could keep the same old formula because it'd no longer be a new Smash that needs to try to outdo the last one, because it'd be 'Smash Online'. It'd be like a recognition of having made the ultimate version of the game so they won't try to one-up that but instead just build out a final free (with the subscription) online version for which content is continually added over time.

With that online version of the Smash we all know and love always there to play, that might even free them up later on like say the following generation, to start a new epoch in Smash and experiment with a new formula for the series since the tried and true Smash would still be available with the online service.

Other than that I really can't think of what they could possibly do to grow the series from literally the 'Ultimate' version. Iterating on the same formula feels like a very 'meh' idea at this point. And totally changing up the formula risks making a misstep and losing the huge audience on one of Nintendo's premier series.

A follow up to smash ultimate will be very difficult for several reasons.
I can't imagine them being able to pull off bringing as many characters in a sequel and that by itself might make it look like an inferior version no matter other potential upgrades.
I don't think Sakurai will return to the series anytime soon and he is for many the face of smash.
There are very few things to improve in ultimate, the online experience is the only part of the game that feels lacking. And I do not see that changing anytime soon since Nintendo are stubborn as hell when it comes to allow certain things (like a working voice chat or more focus on competition) and still have a lot to learn when it comes to building an online experience in general.

I think the series might wait a generation until the next new installment. Even a port or something like an HD-upgrade of Ultimate might be difficult to release due to the licensing nightmare I can imagine.
However, the game is such a money maker that it will be difficult keeping it off the market for long.

Make it like Power Stone and reduce the roster to just Nintendo-published games. You can have the odd one out like something from Astral Chain but mostly familiar Nintendo franchises. I say this as someone who preferred the 3rd party ones in Ultimate but I say do a major change-up.

I shudder at the idea of the next Smash Bros or any installment in the future containing less characters. I am hopeful that licensing agreements can be worked out so that everyone returns and we get more characters in the next game. I am expecting a longer DLC cycle as a result, but I am perfectly fine with that.

Hopefully Sakurai saying that a game like this happening again in the future is his new way of saying "this is my last game". There's plenty of big name third party characters and still a handful of first party characters that could make the cut in the future.

They are going to need to make roster cuts, especially for the third-party characters. The game will probably have one or two more characters overall than Ultimate, but a lot of cuts. Or it could have five less fighters overall, with some newcomers and a lot of cuts.
I don't think we're going to go from 82 fighters (89 including echoes) down to under 60 like many suspect.
Online needs to be improved, but this is dependent on future hardware improvements for online. If Nintendo continues to have trash online, Smash will as well.
There's a very good chance the next Smash isn't really a new Smash at all, and just Ultimate DX with a few changes, a few new fighters, a few new stages, and better performance. Mario Kart did it, why not Smash? Though the big difference there is that Mario Kart 8 was held back by the failure of the Wii U. How much sales potential could you truly get out of Ultimate DX? 10 million units? Yes. 20 million or more? Highly doubtful. Plus, Mario Kart 8 (with or without DLC) still had some opportunity for more content. With Ultimate, it's such a jam-packed game already that slightly more content isn't much of a hook.

I honestly just want new movesets for some fighters, of course new fighters and stages, etc. But what I want most is for the game not to focus so much on the fighting aspect. Yes it is a fighting style game but I think after Brawl each new installment had less to offer in terms of interesting and substantial modes. Let me elaborate.

1.) Make a new Subspace Mode or Adventure Mode that vastly improves upon Emissary. A robust 2D Smash Adventure that spans actual worlds from the in game roster. One that takes full advantage of the IP that only Smash can have. Single player modes haven't been necessarily amazing in any Smash but that can and should change.

2.) Fix Break the Targets. Make a return to the Smash 64 and Melee Era of this mode. Give each fighter their own visually and topographically unique stage that return to teaching you how to utilize a fighter while also being a fun exercise.

3.) Bring back Board the Platforms & Race to the Finish. These were fun, mini obstacle courses that only added to the variety of the titles they appeared in. Of course there is room for improvement for these modes but I think they are worth bringing back. New modes that don't focus solely on fighting would be appreciated.

4.) Spirits are cool but...bring back trophies,

I think once HAL stopped being involved with Smash, the fun side modes that incorporated different game genres ceased. I think Smash is in good hands in terms of the main fighting modes. But I think for the next game, whoever is in charge of development should channel the spirit of the first 3 games while of course adding their own flair to it. I just want Smash to have a better variety of modes in the next entry. The roster will probably take a huge cut but I hope 3rd party juggernauts like Simon, Sephiroth, Hero, Joker, etc. stay in.

I think for the next console at least they’ll just rerelease Ultimate, probably as a Deluxe edition with all DLC characters included and with maybe some tweaks in things like the multiplayer. Yeah there’s the licensing issue for third parties, but I’d think Nintendo has enough pull right now that that shouldn’t be much of a problem.

Yeah this is the crux of it. It's very hard to go bigger than Ultimate, and there isn't much to improve so just iterating again on all the same concepts would just feel uninteresting and risk Smash having much lower sales (as I said in my opening comment I wouldn't bother buying a Smash that just iterates on the 20 year old formula when I can just keep playing Ultimate). Waiting a gen is an option, but not really, as you say it is such a money maker it'd be insane to not bring Smash to the next-gen and waiting a gen doesn't solve anything anyway it just kicks the can down the road.

Yes other than my idea of turning essentially making one last Smash that is a free online game to sell their NSO service and is continually added onto, I think your #1 idea is the main other option. Specifically, really focus on building out a Story mode world.

They've always had some sort of story mode, in Ultimate it was basically just a ton of fights set in an overworld map but it was still very big and took a long time to play through and enjoyable. So yeah the other option for Smash would seem to be just keep the same old iteration on the multiplayer fighting, but really focus on building and selling Smash as a big Story Mode game to playthrough. Like, you have to play through a bunch of the worlds from all the character IP that are included in the game. Make the story mode stand out as worthy of a game purchase by itself, and then people also get the same old Smash fighting that they  love in addition to that. So whereas my idea is Smash Online, this idea could be Smash World.

I suspect Nintendo for it's next console will just do what it did with Mario Kart 8 on the Switch. Include the game and all (most?) of the DLC for $60/$70. With other minor improvements. 

This is a great idea.  I definitely haven't purchased any DLC and would love the opportunity to have all of these fighters/stages.  Of course, they would want to add a new Fighter Pass to go forward as well.  I think they could also give us out of the gate updated characters or stages for games that have come out since then.  I also wouldn't mind some of the extra stuff they had in Brawl like Subspace Emissary and a trophy room.  I'd really like to be able to have a small room to decorate with stickers, posters, trophies, etc that you could win by beating various stages.