The error is correct, you can't run RPCS3 from temporary folders for obvious reasons.
You need to extract it to a permanent directory.
Desktop: Ryzen 7 5800X, Radeon RX 6800 XT, 2x8G DDR4 3600MHz, Manjaro Linux
Laptop: Ryzen 9 5900HX, Radeon RX 6700M, 2x8G DDR4 3200MHz, Manjaro Linux
Old Desktop: AMD FX-8350, Radeon R9 280X, 2x4G DDR3 1600MHz, Manjaro Linux