blue light means bluetooth connection
green light means wifi connection
when windows are booted, then mouse and keyboard can connect in bluetooth mode, but in bios it can connect only with wifi mode
what i recommend - always choose logitech mouses and keyboards, because they also sell wifi connectors separately if you loose any. Other companies doesn't. At once i bought rapoo mouse and keyboard with one connector and lost it. Then i bought same mouse model and that connector didn't worked on my old mouse and keyboard.