While one is still uncertain (rather than do intrusive unlock commands) I suggest to do more simple
fastboot devices
This just gets the phone to self identify serial and mode as
123abc456 fastboot
… ensure the above works before moving on to unlock.
Did you install these drivers also when the phone was in Fastboot mode? Windows might simply install minimal drivers see [Solved] Windows does not see my phone in Fastboot mode.
This would account for < waiting for device >.
“Unauthorised” may or may not still be a problem (please treat them separately)
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I would suggest flip flopping between Install page and the eosinstaller may be problematic for some devices.
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You say you did
In theory this would fix unauthorised (maybe it has). I fit recurs with fastboot devices you may have to follow Fix unauthorized device error in adb.
“Just in case” as you interact, please just look out for a repeat of the “Always allow” pop up
and tick the checkbox, in case it got “forgotten”.