Ideas
I'm also PC/Steam/Xbox Controller and I'm having the same issue. It happens in multiplayer as well as campaign. I played the Beta on both PC and PS5 with controllers, and both platforms felt to me to have the expected level of controller aim assist*.
I suspect that if/when the game detects any mouse or keyboard input while the game is running, it disables the controller-strength aim assist for the entire duration the game stays running.
Try launching the game from Steam, and once the game has launched don't move the mouse or make any key inputs at all, including any keybinds you may have set to a controller such as an Xbox Elite. From my testing it seems that I'm getting proper controller-strength aim assist when doing this. It's hard to test though, even in the campaign. It'd be great if the Firing Range had moving targets.
If this is what's happening, the fix should be to have the game re-enable controller aim assist when detecting controller input. Otherwise, this is pretty broken for all PC controller players. Navigating menus with the mouse or pressing a key to take a screenshot shouldn't penalize us.
*I've read that kb/m actually does have some very weak aim assist, but it's nowhere near as strong as the aim assist meant for controllers. In my testing, it does seem to be that there is a weak aim assist when using my mouse or when encountering this bug with a controller. When not having used kb/m since launching the game, the intended level of controller aim assist seems to be present.