It somewhat depends on the game, and the order that you pair things in.

I’ve run my steam deck, docked on the TV, with 2 Nintendo Pro controllers, 1 XBox controller, 1 Stadia controller, all running over bluetooth, and a fifth PS3 controller plugged in via USB. From what I understand the limit is 8 controllers, but I think the built in controller counts as one.

You can go into the settings and tell it which controller is which, but in the end, the game can override things and make it not work as expected. The only way to really know is to check on a game-by-game basis.