Yeah won't really be worth it with the capture card. I wanted to do something similar with my PS4 and laptop. There are ways to use Remote play without an Internet connection. Perhaps this may be some help https/remoteplay.dl.playstation.net/remoteplay/lang/gb/
I looked into it, but also have a TV so never really needed a laptop as the monitor.
That hdmi port on the laptop is an output not an input. you would need a video capture device to display on the monitor and it will add input lag that will make a fast paced game unplayable or close to it.