There are many different ways to improve older games on a new (much more powerful) hardware:

• no backwards compatibility... probably improved versions for the new hardware later (often for full price) 
• backwards compatibility, but no improvements (besides more stable 30 fps or more stable 60 fps)
• backwards compatibility with minor resolution boost for games with dynamic resolutions
• backwards compatibility with big resolution boost (f.e. 720p -> 1440p or 1080p -> 4K), no other improvements
• backwards compatibility with fps boost (f.e. 30 fps -> 60 fps), no other improvements
• backwards compatibility with resolution and/or fps boost plus other improvements (f.e. better textures, lighting, level of detail to fully use the better hardware)

There are also many different ways to cash in on these improvements (free upgrades, paid upgrades, no upgrade path but new versions).

And of course the platform owner can't force third party publishers how they support the new hardware... BUT they can set a good example with their first party titles.

In the past most "backwards compatible" Nintendo home consoles and handhelds had BC with no improvements (SNES, Wii, WiiU, GBA, DS, 3DS) or very minor improvements (some DS games on DSi, some 3DS games on New 3DS).

But times change and Switch 1 games have to be scalable anyways (docked and undocked mode), so improvements for new hardware should be much easier. Upgrade data (f.e. texture packs, shader compilations) can be easily downloaded and stored on dirty cheap microSD-cards, both for digital Switch games and for physical modules.

Also there are many examples, how the competition handles it:

• many PS4 games got a free PS4 Pro patch/version with improvements, the rest is compatible without improvements
• some PS4 games got a free PS5 patch/version with improvements, the rest is compatible without improvements
• some PS4 games offer a paid upgrade to an improved PS5 version (usually $5 - $15 for the upgrade DLC)
• many Xbox 360 games got a free Xbox One/Series patch/version with improvements, many others are compatible without improvements, some aren't compatible
• many Xbox One games got a free Xbox One X patch/version with improvements, the rest is compatible without improvements
• many Xbox One games got a free Xbox Series patch/version with improvements, the rest is compatible without improvements
• as far as I know there aren't any Xbox One games with a paid upgrade path to an improved Xbox Series version... at least first party
• almost all PC games can use improvements due to more powerful hardware for free... f.e. a Rog Ally can use better settings than a Steam Deck, the Steam Deck 2 will offer much better settings for free, and so forth...

So what are your expectations for the BC on Switch 2 for Nintendo's first party titles?

I would want them to at least go the "PS4 games got a free PS5 patch/version with improvements" route, but this is Nintendo. They will probably do the bare minimum. If there is no BC like, at all, trying to force our hands into buying the games again, I'll probably skip the console altogether, or until it has games that REALLY interest me.

Sorry, I had to shorten the poll answers a lot to see the results better.

Backwards compatibility is like... 99% likely at this point. Both physical and digital.

I think Switch games will use the extra power of the Switch 2 by default. That means:

1. If they use dynamic resolution, it will be more stable and keep at the higher number most of the time (example: Xenoblade 2 runs at a dynamic 360-720p resolution. On Switch 2, it will probably stay at 720p a lot more often, if not at all times).

2. Framerates will be more stable. Games like, say, Bayonetta 3, which aims at 60fps, but consistently falls under 50 or even 40 fps, will probably reach 60 more easily. Games like Age of Calamity will finally run at stable 30 instead of bouncing between 30 and 12 (yes, 12) fps.

3. Loading times, popping and texture loading will probably improve as well. I imagine that games like Batman Arkham Knight and Hogwarts Legacy will GREATLY benefit from this.

Again, this would be just Switch 2 running Switch games without any extra changes. But there's always the possibility that developers decide to update Switch games to take more advantage of the new hardware. Maybe third party games like DOOM, Wolfenstein or The Witcher 3 will get patches to add 60fps options. Who knows.

And obviously, we could also see straight up "remasters" that completely take advantage of the Switch 2 hardware. All of the games above would benefit immensely form this, although it could also be lazy attempts to cash grab.

You're likely to see additional cores being locked out and an underclock to match Switch's frequency and ensure maximum compatibility. A lot of games would be broken otherwise at an engine level so if they do that, it'll vary on a case-to-case basis.

Case in point... the Wii U and the Wii's backwards compatibility. The former being actually worse than running games in OG hardware due to a poor upscaling solution.

But it should run at least equal to docked specs in portable mode, at least.

Nintendo? BC with absolutely zero improvements.

Edit

I should say I'm 100% fine with the above statement, I just want BC.  No BC would be a disappointment.

What I think they'll do is, have more or less 100% backwards compatibility, but with no improvements for any games, and then they'll probably try to sell upgraded versions of a few games, like the Zeldas or Smash Ultimates and such.

What I want them to do is have full backwards compatibility with free upgrades for as many games as possible. Which extends to my wider belief that when you buy a game, you should own it - on every platform it's on, period. But that's a topic for another day.

Like it was said above, a lot of games on switch use dynamic resolution and if run on more powerful hardware they will stay on the higher end of the range.  A Loty of games would also be able to run at their intended FPS. They will be improvements just on that even if they don't do anything.

I think the backwards compatibility solution will be different than the Wii U one. Instead of running the games inside a "Switch 1 OS" and in a literal 1:1 state, the Switch 2 will most likely follow the PS5 approach: run Switch 1 games with the enhanced hardware of Switch 2

The majority of these are just the PS4 Pro version running on the PS5 (worse in some cases, better in others). The rest was either designed with a PS5 mode in mind (2019-2020 titles) or that received updates from their developers later on.