The below is predicated on the Computer itself has already been upGraded to Monterey.
If that has not been done the below would be applicable.
There are reports appearing on the ASC Forums regarding failed installation of Monterey on older Qualifying Apple Computers. In most cases this is related to having a NON Apple Original internal drive ?
And, in your case the External Drive would be the root cause of this behaviour.
The EFI Boot ROM included in Monterey is verifying for Original Apple Drive and if not found , may Balk or fail to upgrade to Monterey.
Reports indicate the EFI BOOT ROM is Required to Flash the Computer and is a requirement for a Successful Monterey Installation.