The steam machine should probably be able to handle PS3 emulation just fine,my old Ryzen 3600 could run RPCS3 with only minor issues and the Steam Machine CPU is significantly better.
But for building a pc, for just PS3 and less even a 9600x will do just fine. Maybe stretch to a 9700x to be safe if you're wanting to run games at much higher FPS than they ran on the original PS3.
Emulators are not GPU heavy. The 9060XT 16gb is a great bang for your buck GPU right now but even picking up an old RTX 3060 12gb would more than do the job for 4k PS3 emulation.
Sonic Unleashed has actually been recompiled so you can get a native version of it that will run much better than emulation.







