There's practically nothing recorded above 60fps to watch on that second monitor. YT, Twitch, etc all cap at 60 fps. Even the tv's that advertise true 120 hz refresh rates aren't actually displaying 120 true frames. They're typically getting 60 fps or even 30 fps content and then interpolating the extra frames. So I'd say 144hz would be a complete waste for a browsing/video monitor. 1440p or 4k might be worth it to you. More screen real estate for extra windows, and you can find 1440p and 4k content on YT and Netflix and so forth.
For the gaming monitor, 1440p@144hz absolutely.