Is your RX 480 4gb or 8gb variant?
The first thing that comes to my mind is moving to a newer platform.
CSGO and APEX are more CPU than GPU demanding, since they are first person shooters.
Your RX 480 can still game Rust and all of the new title's atleast on 1080p low/medium.
Something like this should make a significant improvement in gaming performance, and overall usage:
PCPartPicker Part List
CPU: Intel Core i5-10400F 2.9 GHz 6-Core Processor ($149.00 @ Amazon)
CPU Cooler: ARCTIC Freezer 34 eSports DUO CPU Cooler ($39.99 @ Amazon)
Motherboard: ASRock B460 Phantom Gaming 4 ATX LGA1200 Motherboard ($92.99 @ Newegg)
Memory: Corsair Vengeance LPX 16 GB (2 x 8 GB) DDR4-3200 CL16 Memory ($89.99 @ Amazon)
Storage: Samsung 860 Evo 250 GB 2.5" Solid State Drive ($49.99 @ Best Buy)
Total: $421.96
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2021-03-13 06:37 EST-0500
i5 10400F is a 6 core 12 thread cpu that matches the Ryzen 5 3600 in performance. Ryzen 5 3600 being a much more expensive cpu makes no sense for this build in my opinion.
The stock cooler for the 10400F would have been enough, but stock coolers tend to run really loud and not cool that good.
A arctic freezer 34 Esports DUO will both keep you cpu really cool when gaming while being really silent.
The motherboard is solid for a 10400F. 10400F isnt a needy cpu so no reason to go overkill on the motherboard, a ATX formfactor with all of the fancy features for under $100 sounds really good imo.
The ram is classic for now, 2x8gb 16gb 3200mhz. Shouldn't have any problems running programs in background while gaming.
The Samsung 860 EVO 250gb is a perfect ssd for reviving old system. Enough for windows, but always room for some games.
Although i would just put Windows on this SSD and put all of your games on your 1TB HDD.
^ all of this should significantly improve both your gaming and operating experience.
Edit: You can keep your cpu since this upgrade will actually consume less wattage than your FX system.
Keep the psu until you decide to upgrade your GPU.