I have the exact same issue. I fixed the achievement problem by running ubisoft connect as right click -> run as administrator. But the game does not start. GRB_vulkan.exe is in my process list, using like 15 megabytes of memory and just stays that way. No Battleye launching or anything. I tried launching BE from the folder directly and also the regular GRB.exe, none of them worked.
I reinstalled the entire game and ubisoft connect too. Cleared the spool folder. Nothing solved it.