Spoke to Apple Support; apparently it's a known issue. Their advice (which did solve the problem) was: Unpair Apple Watch from iPhone Sign out of iCloud on Mac Sign back in to iCloud on Mac Re-pair Watch and restore from backup. And you really do need to wait until your Watch is absolutely restored, before the option appears in the Security & Privacy screen. That said... the feature is extremely flaky. 90% of the time, I get the message "Unlocking with Apple Watch" before being presented with the password text box. Pffft.
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