I have a lead on a used 4060-Ti right now for about $250 that I'd be replacing my old 6600-XT with. According to user benchmark it's a significant upgrade, but I'm not sure the upgrade is worth that much. The 6600-XT struggles a bit more than I'd like at 2k in some games like Star Citizen (don't laugh please), Baldur's Gate, Cyberpunk 2077, etc. Even FFXIV can chug a little in certain areas. I'd be using it for somewhere like 3-6 months while I save up for my dream PC as a stop-gap.
Otherwise the computer has 32 GB DDR4 RAM (not sure on clock speed) and a Ryzen 7 5700G. I don't really think either of those are the bottleneck.
EDIT: I have been informed that UserBenchmark is garbage and that I've been working off of bad info. I'm probably gonna go with a 6800XT or 6900XT for an interim upgrade instead.
https://gpu.userbenchmark.com/Compare/Nvidia-RTX-4060-Ti-vs-AMD-RX-6600-XT/4149vs4117