Ye that is how I use multiple monitors too. 2nd monitor has something I use like 5 minutes to the hour, like Spotify etc.

what does a 4k screen do for productivity? i get the image is clearer than 1080p but is it worth the higher spend?

Depends on how you run it. A screen is more than just "4k", or 4000 pixels wide. The amount of pixels in total spread out over the physical dimension, depending on the aspect ratio and the distance between you and the screen as well as the rendered density by the computer together make the result.

So, you could use a 27 inch 4k display at 16:9 aspect ratio (which is 3840 by 2160 pixels) in a way that gets you the native resolution which results in much more usable space but the displayed quality isn't all that great. You can run them at 2560x1440 rendering which sacrifices some pace for much improved quality. Works well when you don't sit super close to your screen. Or, if you like more space but still have a little better quality than the jagged mess that is the native resolution, you could run it at 3008x1692. Close to fully usable space but still way better in terms of quality.

The scale of your computer rendered interface and text versus the actual pixel size and density on your display gives you a balance to choose from for space vs. quality. Which one works best is a combination between physical distance to the screen and personal preference (which mostly forms based on cognitive load).

My experience, after buying a monitor for home for the first time in like a decade and getting a very nice 27" HP z27 4K: it's... fine. I think I'd need like 5 more diagonal inches before I could really fit more on it than I can on a lower-pixel-count 16:10 monitor the same size. Because of the way scaling works, what I want is everything scaled to about 1.5x, but that's computationally expensive and/or looks bad, so in practice I run at 2x anyway, so the benefits in stuff-on-screen aren't really that high. I can keep fonts set a little smaller I guess.

I kinda regret not getting 2x 1440p monitors with similar picture quality for less money.

Meanwhile it makes using Linux a giant pain in the ass, unless you go all-in on a major desktop on a major distro, and then also get lucky. Possibly I'd have a better opinion of it if I were using it with macOS rather than Win10 and Linux.

[EDIT] and OMG lacking auto-temp-control based on surrounding light has me really wishing I'd just put the monitor cash toward an iMac. Way more eye strain.

install redshift or something similar. it's basically flux

It lets you fit more stuff on the screen, legibly.