I had this exact same error:
“Another update is currently in progress” but no core_updater.lock in _options table
I finally figured out that my database had a few tables that were not set to auto increment the Primary ID
This condition usually results in the latest record to have an ID of zero, and THEN no more records can be added to that table.
Screws up a lot of things especially if the wp_options table is the culprit.
So I fixed that setting for the tables that matter, and all seems to be good now.`
WordPress update to 6.02 installed fine after the fix
Sam