Elgato Cam Link 4K Camera does not show up inside import dialog

I am using the newest FCP software in trial mode for Mac. A Sony a6000 is connected via Cam-Link 4K in 1080p50 mode.

Unfortunately the camera does not show up inside the import dialog like e.g. the Facetime camera does. I tried it on another Mac (mini 2021) with a fresh install and I exchanged the capture card for another brand. None of them bring up the camera. Photo Booth and other software does show the camera on the same system. I rebootet as well with only FCP running. Same result.

How can I show the camera inside the import dialog in order to record directly from it?