The cap may be loose, it is not integrated with the stick. This problem may occur during transportation.

In the vertical direction, press down slightly, which just helped a user solve this problem.

Steam Deck Connection

• 1. Update your Steam Deck to the latest version.
• 2. Connect the controller to your Steam Deck in Xinput mode to play.     
• There’s a switch button on the back of the controller. And you don’t need to use the adapter.

As far as I know, it can only connect SD through xinput, you can test which kind of input it is.