It shouldn't be a problem to run 5700XT and 6600 on the same rig with 21.10.2. The latest drivers will have problems only with very old cards like Baffin or Gfx804 (RX 460/550/560), or anything older than Polaris. Polaris cards (RX 470/480/570/580/590), Vega, RX5x00, and RX6x00 cards will work fine with the latest drivers. We haven't tested with 6600 yet but the we managed to order a few of them so we will be able to confirm that they work in a week or so.
It is good to know and thank you for the advise. Normally I don't use AMD driver when it is released immediately as I had bad experience with 21.4.1 and 21.5.1 with 5700XT. I will try it out soon.