Big Sur - Unlocking with Apple Watch

I had the same issue with Apple Watch 6 (watchOS 7.1) and MacBook Pro 13 early 2015 (Big Sur). So I repaired it with some steps:

1) I disabled Keychain synchronisation on MacBook (Settings/iCloud/Keychain)

2) I made steps in this thread https://discussions.apple.com/thread/251803595?answerId=253458029022#253458029022

• • Open "Keychain Access"
  • In "View", enable "Show Invisible Items"
  • Search for "Auto Unlock"
  • You should see a whole bunch of application passwords for "Auto Unlock: XXXX's ..."
  • Select all records and delete (this will reset/disable auto unlock on other Macs if you use multiple Macs)
  • Whilst still in "Keychain Access", search for "AutoUnlock" (no space)
  • There should be 4 entries for "tlk" "tlk-nonsync" "classA" "classC"
  • Select 4 records and delete (don't worry if they re-appear, the system repairs this automatically)
  • Open "Finder" and navigate to "~/Library/Sharing/AutoUnlock"
  • There should be two files "ltk.plist" and "pairing-records.plist"
  • Delete both files

3) Disconnected Watch from iPhone

4) Connected back Watch to iPhone (set it from backup)

5) Restarted MacBook

6) Turned on Keychain in iCloud settings

7) Enabled Auto Unlock for Watch in System Prefs