Yes, internal consumer capture cards are not really supported on Linux, the manufacturers just don’t care so no Linux drivers are available.
That’s why I have gotten myself a prosumer grade card from Blackmagic. https://www.blackmagicdesign.com/products/intensitypro4k
Or you could use USB Capture Cards which are better supported, because most of them act like a USB camera, using the same protocol which eliminates the need for drivers, but they often are more limited or have a worse picture quality then internal cards.
Yes, it does perfectly fine here. Blackmagic is known for its Linux support