amazon web services – RDS Postgres could not be upgraded because one or more databases do not allow connections

I’m using AWS RDS to run a Postgres server, and I’m trying to do a major upgrade from 9.6.11 to 10.15. I’m using aws-cli to request the upgrade, like this:

aws rds modify-db-instance
  --db-instance-identifier my-database
  --engine-version 10.15
  --db-parameter-group-name my-pg10
  --option-group-name my-pg10
  --allow-major-version-upgrade
  --apply-immediately

The database changes from “Available” into “Upgrading” state, then 2-3 minutes later it goes back to “Available” and the version is unchanged. A new file called error/pg_upgrade_precheck.log.1613891689533 appears in the logs tab, and the content looks like this:

------------------------------------------------------------------
Upgrade could not be run on Sun Feb 21 07:14:49 2021
------------------------------------------------------------------
The instance could not be upgraded from 9.6.11.R1 to 10.15.R1 because of following reasons.
Please take appropriate action on databases that have usages incompatible with requested
major engine version upgrade and try again.
- The instance could not be upgraded because one or more databases do not allow connections. 
Please ensure all non-template0 databases allow connections and try again.
----------------------- END OF LOG ----------------------

I tried doing a major upgrade to a different version (10.7) and that failed the same way. I tried doing a minor upgrade to 9.6.20 and that worked just fine.

I’m stumped. How do I make progress upgrading this database?