Best way to play consoles on PC monitor, but with audio coming through headphones from PC?

I have a multiple monitor setup on my PC, but want a way to play consoles on one of the monitors.

I know I can just plug the HDMI into the monitor, but that would make the audio come through the monitor's speakers. I would prefer to have the audio come through the PC headphones so I can have a game on one screen any other stuff on another monitor and have audio from both.

I understand capture cards could be used, but they have lag and would be bad for fast paced games.

So is there a good way to do this, or do I have to just deal with either of these options?