Need some advice for PC upgrade

Hey everyone. I'm currently running a Ryzen 5 5600 and a 9070XT on a 1440P monitor, and I do want to eventually upgrade, which is why I was thinking I may as well buy the CPU for now, and buy the RAM later once prices drop a bit where I live.

I mostly use my PC for gaming and web browsing so I was looking at the 7800X3D since it's around 320USD, whereas the 9800X3D is closer to 450USD, but don't know if there's any other CPU worth looking at.

I was thinking of maybe just waiting it out until AM6 but I don't see it coming any time soon, so might as well just make the jump sooner rather than later.

Would appreciate any advice!