I think they'll disable hardware in compatibility mode because OG Switch games won't use it. Switch games are only designed to use 4 CPU cores (well, 3 actually, with one for the OS) so there's no point giving them 8. On the GPU side, games are expecting 2 SMs, and although I sort of suspect there might be a bit more scope to spread work across more SMs, but it's probably opening a can of worms of potential issues by trying to create a solution which works across every game. You could do it for games using OpenGL or Vulkan, but they're likely only used by games which were never pushing the graphical envelope in the first place. The simplest solution is to just use 4 CPU cores and 2 SMs and leave it at that.
I suppose it's partly that I just don't think the benefits of "turbo mode" BC would be enough to be a significant selling point for the console. Of course this is all subjective, and I'd appreciate a more stable framerate in Link's Awakening as much as anyone, but I don't think the fact that you can play some existing games at a slightly improved framerate or resolution is a big selling point for a next-gen console.
The scope of the benefits you'd be able to achieve is important here. For games which maintain consistent resolutions and framerates already (which includes many of the best-selling titles on the system) the benefit is zero. Then you've got games which don't quite maintain a solid framerate or come in just below peak resolution when using DRS, which would receive a noticeable, but not major boost. For games that have big issues, either in framerate or extremely low resolutions, I don't think Nintendo will be able to do as much with straightforward BC as many people seem to expect.
People's expectations for BC improvements come from PS5 and XBSX, and I think it's worth comparing those to Switch 2's situation. On PS5, the BC implementation uses the PS4 Pro version of the game if one exists, which means a game designed for 8 CPU cores and a 36 CU GPU. The PS5 has an identically-sized 36 CU GPU, running at as much as 2.5x the clock speeds of the PS4 Pro, and an 8 core CPU that's far more powerful than PS4P. That means that a PS4 game running in boost mode can use the full PS5 GPU and CPU with huge performance improvements on both sides. Even games without a PS4 Pro version will benefit from massively higher clock speeds on the GPU side, and a similar CPU boost.
For Xbox Series X, MS have gone with just 30% more CUs in the GPU over Xbox One X (although with a less significant clock speed boost), and a similar jump to a far more powerful 8 core CPU. So Xbox One games (with One X versions) running in BC are able to use around 77% of the Series X's GPU shader performance.
With Switch 2, Nintendo have gone pretty much the opposite direction that MS and Sony did with their consoles, and instead of a similar size GPU with much higher clock speeds, we have a far larger GPU with likely much more modest clock speed improvements. With a GPU that's 6 times as big as Switch's (and no Switch Pro to have prepped games for bigger GPUs), games running in BC mode are only going to be able to leverage 17% of the console's shader hardware, compared to 100% on the PS5 and 77% on the XBSX. As much as Switch 2's hardware is a huge leap over the original Switch, original Switch games aren't going to be able to use the majority of that.
The CPU side will be better, between big performance-per-clock improvements and moderately higher clocks, so I'd imagine most CPU-limited games should be generally ok, but I'd expect games which are limited by the GPU to get nowhere near the boost we see on PS5 and XBSX.
I honestly wouldn't be surprised if Nintendo don't even mention any performance improvements from BC, instead focussing on games which are patched to properly utilise the new hardware. That's not to say I think battery life in BC mode would be a major part of their marketing or anything, but I could definitely see their spec sheet listing, say 3-6 hours on Switch 2 titles and 8-12 on OG Switch games, which would be enough to get picked up by press and perhaps dampen some of the impact of it not having quite as much battery life as current Switch models do.