Q: Do monitors with higher refresh rates require a faster GPU, or is the resolution you run in more important (for games, specifically)? Or are both important? I guess that's two/three questions.

The following is just rambling backstory, if you are interested in my dilemma:
I currently have an old Geforce GTX 760 running an old 24" 1080p 60Hz monitor. Up until recently, I have had no problems running any games that I have been interested enough to install and play. Not being able to play games with most if not all graphical goodies turned on, has kind of always been the signal to myself that it was time to upgrade Ye Olde Graphics Carde, but now, you can't even find decent cards in stock for reasonable prices!

I built a second computer for RoF (Rest of Family), and so removed one of my two 24" monitors from my main, gaming/working rig. And going from two monitors to one is painful, especially since I have been doing a LOT of photo editing lately, and having that extra monitor for previews and such was amazing and very efficient.
After much and I mean MUCH research and forum chatting and reading, I have decided that the best monitor path forward for my main/gaming/work rig is the following:
1. A 27" 4K monitor, with very good color, IPS - refresh rate not important (editing/productivity/web browsing monitor)
AND
2. A 30/32/34" VA monitor at something below 4K resolution, with something at or above a 100Hz refresh rate (gaming monitor)
The problem as you might have already guessed, is that I can't find a decently price video card that will run 2. above. I was all set to buy a 1660 quite a while ago (which I am kicking myself now for not doing), while they were in stock, and not being ridiculously overpriced due to demand, but I saw that RTX cards were coming out, and multiple sources were saying WAIT!!!! DO NOT BUY NOW!!! There's a new card coming that will be CHEAPER than the current RTX card, AND FASTER BY A LOT!!!

So here I am, assuming that the supply/demand and production issues that are wreaking havoc on the GPU market, will continue for at least another 8-12 months.
I'm really MORE interested in just adding the larger gaming monitor at this point (2. above), as I have a pretty decent (but smallish) 24" IPS monitor that I use for everything now. So that means I need to consider the limitations of my current video card wrt the potential new monitor. Considering I am coming from 60Hz, I am totally fine with a 100Hz gaming monitor, ESPECIALLY if that means that I could get by with my current card for a while. But if 144Hz (much more common, now) is more demanding on the GPU than lower refresh rates, then that narrows my search.
Please OO, you''re my only hope! (imagine me wrapped in a sheet saying that in a low res, ghostly image)