Correct me if I'm wrong, but a big reason why a platform would have a mid-gen refresh has to do with interest in the original platform, right? If a platform is showing a slowing of sales, then that becomes a push to bring something out that would increase interest. Sure, a platform does go through multiple SKUs, but for those, it never really does anything but optimize what already exists, like lowering power consumption, make the unit smaller, etc. The refreshes tend to bring something new or improve, like 4K with PS4 Pro and XB1X, but in Nintendo's case, imo, it usually has to do with gimmicks to accompany what they improve.
Unless I'm mistaken, there have been only 2 generations where Nintendo had mid-gen refreshes. The DS and the 3DS, being the DSi and n3DS respectfully. In both cases, the focus wasn't about power, but power is what was required for the inclusion of what they featured. With the DSi, they added a inner-facing camera, a digital store, and a web browser built in (as opposed to the GBA cart method). The use of those requires an increase in CPU power (to 133Mhz, 2x the original), RAM capacity (to 16MB, 4x the original), and the need for internal storage (256MB, new). I don't think any game outside of digital and DSi-specified carts utilized the faster CPU to boost performance.
With the the n3DS, the main focus was the inclusion of super-stable 3D. I don't know exactly how much processing the SS3D required, but it seemed it not only needed its own core that wasn't shared with anything else, but the base frequency wasn't enough for that either. So they increased the CPU power (to 804Mhz, 3x the original), increased the core count (4-cores, 2x the original, which I imagine they couldn't have 3-cores by design or the cost difference of 4 was negligible), and increased the RAM capacity (256MB, 2x the original). It also got a boost to VRAM from 6MB to 10MB, but I don't know if that was required for SS3D. While they were at it, they included the functionality of the CPP to add the extra shoulder buttons and a c-nub in place of the other circle pad. Various games do utilize the increased CPU power (MH4U for more stable frame rate and faster load times), increased RAM (Smash Bros so it didn't have to swap out the OS), and others.
The thing I'm pointing out is that with Nintendo, the general reason for improved specs with a mid-gen refresh wasn't for the games to run better, even if it resulted in that. It was to handle whatever gimmicks they included, to grab people's attention for a platform that was showing signs of slowing down early on. This is why, imo, Switch never got a mid-gen refresh, regardless if one was planned. When other platforms saw slowing of sales a few years after the initial launch, Switch kept its pace, and even went faster. It's only now that sales are slowing down, but we are deep into the 6th year (5 full years plus most of the 6th), which is around the time we would expect a successor to come around. It's why I feel the idea that a mid-gen refresh was never planned for this time now ('22 - '23), and that if it was ever planned, it was meant for years ago.
There's also something about the prior mid-gen refreshes. In both cases, the hardware was improved, but was never changed out for something different. I mean, with the DSi, it used the same ARM9 CPU, just at a higher frequency. With the n3DS, it used the same ARM11 CPU, just at a high frequency and more cores. GPU was not touched (besides the VRAM in the n3DS). This is likely due to the need to keep compatibility with existing titles. So what about a supposed Switch mid-gen refresh? In all honesty, what could they use? Basically using anything that wasn't a TX1(+) might mean incompatibilities in at least one category, mainly the GPU if the architecture of predecessors differs enough, where the need to translate calls (and handle shaders) would be required. Would the TX2 even be a candidate when it has the same 4-core A57s?