Ok, I gave the "2 USB-C" configuration yet another try. No go. Zilch!
Next I tried 2 different USB-C monitors and again... Nada! The problem is that the "other" monitor is an "el cheapo" portable one (that I use on the road with my Macbook), that probably also lacks a proper identification. So there is no way to be 100% sure of the culprit here.
That said, time to get back to the HDMI+USB-C.... oh boy, that was a nightmare. Had to perform the workaround twice, and I even added a second shutdown/boot cycle with just the HDMI attached. Sounds like it needs to "record" which monitor is booting (seem to remember). If the mini boots on the USB-C it will not work. Need to boot on the HDMI. Why? No F clue.
Aynway, this behavior with different monitors makes me believe that there is much more going on under the hood here. But right now I'm happy that I can get both monitors to work, sleep/wake seems to be working, I'm seeing no screen positioning swap and I have an extra USB-C port (add a second external drive?) free. I don't mind the setup but the color profiles are not matching. I need to perform a new calibration, but for most uses, it's ok (bugs me because I use an 8K wallpaper over 2 4K monitors, so I do notice the difference of the color tones). But that is solvable (and I can live with that).
Will see what happens with the Mac Studio, soon!