I’ll occasionally switch to that as it shows up better on projection screens for presentations, but it’s not my default.

You may want something like https://jetkvm.com/ or https://pikvm.org/. They will do the video capture and keyboard/mouse input.

Also check out https://symless.com/synergy. I really like it for using my work laptop next to my desktop. It doesn’t do video, but extends your mouse and keyboard to other computers.