So now that 12.2 is out in the wild, I can be a bit more specific. 12.2.0 is still Intel-only. There just wasn't enough bandwith the finish all the new cross-platform features and put together a polished ARM port. However, if you know where to look (very carefully), it does know whether it is running on Apple Silicon or an Intel CPU. I'll leave that as a little Easter egg for folk to find. As for when the native port will be available, I can't say definitively when, but this will not be like the Cocoa port that took years to finish.
We are running the full QA validation suite on a real M1 Mac as I write this. Thus far, the only issue we've found is with Metal. If you use transparency in Graphics3D, bad things will happen. Workarounds include turning off antialiasing, as well as going into the options inspector changing 3DRenderingEngine to OpenGL instead of Metal.
And about MKL specifically, it runs quite will on the M1 Mac. Rosetta does not emulate certain newer instructions (AVX, AVX2, and AVX512), but it emulates a slightly older Intel CPU well enough that MKL can't tell the difference and gives good performance.