Backup option is greyed out after restart; cannot back up

I would suspect the communication between the computer and the drive got interrupted for whatever reason, but unplugging and reconnecting it sorted it out. Hence the drive became visible again and thus the backup became enabled.

I get something similar very occasionally with my MyPassport drive - plug it in and it powers on but Windows doesn’t see it. But unplugging it and plugging it back in again gets it working fine. I would guess either Windows is busy with something else and hasn’t started the driver yet, or some similar issue which is stopping it getting started. In my case I think it’s more a Windows issue than anything else (given how busy Windows tends to get just after a reboot getting all the baggage that typical installs tend to accumulate started up and running) and I would only be concerned if it starts happening more randomly during normal operations rather than just specifically after a reboot.

But at least all is up and going again now, which is the main thing. If it does recur then I would look at the drivers, or if it’s specifically at reboots perhaps review what you have set up to start in such occasions.