Should I Upgrade My PC or Build a New One for FPS Gaming?

I'm currently using an RX 6600 and a Ryzen 5 5600 with 16GB of RAM, and I've got about $1600 to either upgrade my existing setup or build a completely new PC. If I go the route of building a new rig, I might sell my old parts and increase my budget to around $2000. My primary use case is playing various competitive FPS games, including titles beyond just CS:GO. I'm not involved in activities like video editing or streaming. I live in Sweden, which might factor into parts availability. Just as a heads-up, I have an Odyssey G5 monitor that supports 2560x1440 at 180Hz. I often face low and inconsistent frame rates in games like Tarkov and BF6, even with low settings, which has me reconsidering my setup. Any advice would be appreciated!