With the recent AMD launch of the 7000 series CPU on the AM4, the older AM3 is cheaper.
The upgrade path doesn't exist for the AM3 builds, but they're going to be cheaper since they also use DDR4mmemory.
Something like the Ryzen 5 5800x3d with the extra cache, was the best gaming CPU until the recent Ryzen 7 7800x3d.
The 5800x3d is probably $300 now, a B550 mother board can be had for around 120 with wifi, or even cheaper without wifi. The DDR4 4000 speed memory for 16 gigs is probably less than $100 and a RX 6650 XT, GPU which will do 1080p gaming is probably around $300. Swapping out a a non X3D Ryzen will probably be 50 bucks cheaper. Or hell a Ryzen 7 5700G with the built in IGPU might do 1080p gaming now.
https://pcpartpicker.com/guide/
Can be helpful too.
The 12th gen Intel, still uses DDR4 too, which means cheaper mother board and memory as well.