but the other question is, why no controller support on the PC version ?
As UI has been in constant development, my guess would be that they wait with controller support, until they finalise UI. However, as far as I understand Stadia version had some form of controller support, so

YES, they were developing for STADIA so they should already have had controller support b/c it was going to release at the same time as on PC--hmm whatever happened to that code, I really hope its in the final version, perhaps it will play better with controller.
I played Cyberpunk 2077 on STADIA with their controller and it was GREAT! They have refunded my purchase for the game and controller/dongle since they are shutdown now.