Yeah, nothing wrong with wanting an upgrade, as long as you're doing it for the right reasons.
Ok, so a 390 should be somewhere around a 1650 to 1650 Super or 5500 to 5500 XT. If that's still good enough keep it, if not, unless you need a huge upgrade, a used GPU will probably be cheaper.
I think you could and should reuse everything apart from CPU, RAM, and mobo. If there's nothing wrong with your HDD/SSD, PSU, cooler, and case, then I would keep them unless you're trying to sell the entire old build.
Maybe add a new NVMe SSD, but that's it.
GPU encoding would mean basically no CPU load, and that obviously makes a huge difference for a CPU-bound emulator.
https://www.youtube.com/watch?v=CLqpVImLPGE&t=305s
https://www.youtube.com/watch?v=H0pCpNT4b-Q&t=620s
Basically, thanks to NVENC (the nVidia hardware encoder), CPU encoding (x264 in particular) for streaming stopped being worth it years ago. By now AMD (AMF, formerly VCE) has caught up and even surpassed nVidia in some cases, but it's pretty even. And then there's Intel Quick Sync. It's the one thing the Intel GPUs do really, really well, because they do it better than anyone else. It beats x264 medium preset. You can not afford a CPU that would even run a 1080p 60 fps stream via x264 without choking the emulator completely.
So I do highly recommend going this route.
Yeah, if CXBX still doesn't like Ryzen, and you're fine with GPU encoding and don't want to overclock, then there's no reason not to get an Intel CPU.
Again, the i3-13100 would be a fine upgrade. Should be roughly 80% faster single threaded and you do get 8 threads instead of just 4 as with the 4690K. Still 4 actual cores though. 3.4 GHz base clock, 4.5 boost. 190 CAD.
Then there's a couple of i5s. All with 6 big cores (12 threads), but the i5-13400 only gets 4 small cores on top, the others get 8. Not going to matter unless you go for something highly multithreaded (18+ threads), but worth keeping in mind anyway.
Anyway, so the 13400, 13500, 13600, and 13600K get 2.5/2.5/2.7/3.5 base clock (1.8/1.8/2.0 for the small cores), 4.6/4.8/5.0/5.1 boost.
With the 13400 at 310-320 CAD and the 13500 at 330 CAD, I'm going to declare the 13400 to be pretty pointless.
The 13600 is for some reason not available at all and the 13600K costs 410 CAD, which really isn't worth it if you're not overclocking.
The lower base clocks are to fit 6+ cores into 65W TDP, while at boost clocks they're allowed to draw >150W. Most mobos have very generous settings in that regard by default, and if not it's easily fixed, so I'd mostly pay attention to the boost clocks.
So the 13500/13600 should be 6-11% faster even single threaded than the 13100 when properly cooled, but paying 75-100% (if you can find a 13600) is obviously only worth it if you're actually getting something out of the extra cores.
For CS:GO, TF2, and Dota, I don't they'd matter, but they can be nice for newer games and e.g. Counter Strike 2 performance might be of interest to you, since you're getting it for free.
I could've made this a lot shorter, but I want you to be able to make an informed decision instead of just slapping down "get an i3-13100 or i5-13600 and use Quick Sync" and leaving it at that.