This has been solved by logical replication a few versions ago.

1. Leave your old database running

2. Start your new database with new version

3. Run logical replication and let it catch up

4. Decide you want to switch over.

5. Using a script: Stop your apps writing to the database (or switch to read only mode), let logical replication catch up one final time, stop logical replication, run a procedure to fix your sequences, and switch your apps over to the new database.

You are now done. Sure, it requires a one-time investment to work out the exact steps needed for your situation, but it's easy to do with minimal downtime.

Of course if you don't care about downtime just shut down your database server, make a backup(!), and then do pg_upgrade.