I know that the difference between 144hz and 240hz is small yet significant, is color accuracy the same way?
Is there significant difference between TN and VA Monitors? Or is it too slight to even care much?
VA monitors have better Viewing Angles and Color Accuracy and deeper blacks so higher contrast. They are in between IPS and TN.
For photoshop I would say go for a IPS pannel. It'll be good for gaming and photoshop. They have the widest viewing angles of the 3 displays so they retain color accuracy no matter what angle you look. I can't stand TN panels. The picture just looks horrible on them because of this viewing angle thing, they loose colors and look under saturated at an angle. I have all 3 and my favorite is IPS.
Your games will look better too picture quality wise with IPS. For photoshop you can also get away with a VA panel since you're sitting center and looking at the screen dead on. So viewing angle might not be a problem with VA plus you get higher contrast.
I would say go for IPS 144hz, 1440p, above 90% Srgb coverage, and low input lag and that comes pre calibrated from factory so you won't have to buy an color analyzer meter to calibrate your screen, those are expensive. Some Displays even include a certificate that it has been calibrated for accurate colors. Practically every reviewer includes color accuracy in their review so you can look at that to find a color accurate monitor.
And that resolution bump from 1080p will make things look sharper. 1080p is too low for me. And 1440p is a good middle ground between 4k and 1080p that will make your games look good without having a high end graphics card to power 4k gaming.
For high end color monitor you can go for above 90% Adobe RGB coverage which can display more colors, but you can get away with just Srgb coverage for photoshop if you are not a photographer and just a hobbyist. And they are cheaper too. The majority of stuff runs in Srgb anyways, internet, youtube, movies its all mostly in Srgb.