Technically, all the boot options were on the same drive (same EFI partition, on the disk that was initially used for years by windows), but for some reason, the motherboard decided “nope, there’s no bootloader there”.

I ended up repartitioning the “first” drive seen by the bios to make a 100MB partition at the beginning, named it “EFI system partition”, copied all the content of the old one from the other drive, and nuked the actual windows install in the process (not the boot entry though). Now all is good… I hope :D