Rest of your system seems balanced enough. What settings are you playing at? Max? Check out this review. On one page they show the RX 580 getting 59 fps at very high details.
https://www.guru3d.com/articles_pages/shadow_of_the_tomb_raider_pc_graphics_performance_benchmark_review,6.html
Before you purchase anything, try to turn the settings back just a little and see what it does. You could use fraps to measure your fps.
If you only get 59fps like the benchmark, then monitor is theoretically ok. But when you start getting into the higher cards and get say 80-100+ fps, then the screen tearing I think would be more of a thing.
I guess looking at it, turn your settings to high or medium. It my theory is right, you should get an idea what the screen tearing looks like that way. Then if you don't mind it, then upgrade the card first. If you have the screen tearing, then maybe go for the monitor.
You are at kind of a catch 22 if that makes sense imo.