I thought your monitor supports only 60Hz at 1080p? If you're looking to squeeze more FPS out of your current GPU, then only upgrading the processor will do. The 5600X (or if there's 5600 instead --I'm not up to date with the current Ryzen lineup) is a good choice. Better single-threaded performance all around, even compared to 10th gen Intel or Ryzen 3000 series which matters most for the vast majority of games still.
Not sure if either Windows or AMD has updated this, but I recall 1 CCX Ryzens to have better performance in gaming than the x600 series due to some strange inter-CCX communication scheduler that allows lower-end Ryzen like 3100 and 3300 (also X variants) to have great performance even compared to a 12-thread 3600 (beating even the 2600 and 3500/X). If they have, then only Ryzen 5000 will net you tangible gains in FPS, otherwise, there is an option for the 3300X since it damn well matches the performance of a stock 7700K.