The programmer and new esp01s arrived from aliexpress. Got it up and running within 5 minutes following Add Wifi to SKR Pro step by step
I used esptool.py from the extra/esptool package on Arch Linux to do the firmware flash. (esptool.py -p /dev/ttyUSB1 write_flash 0x00000 firmware.bin)
I haven’t connected it to the cnc yet though, I won’t have time to do so until somewhere next week.
[EDIT]
I just tried to flash the original esp01s I had, and it seems to be dead, the esptool can’t connect to it. But that could very well be my own fault, I gave it 5V when trying to get it running before (after it wouldn’t show me a SSID on 3.3V).