Recommended procedure to remove old files after major version PostgreSQL database cluster upgrade
One thing to be very careful about here is whether you’ve done a pg_dump+pg_restore or a pg_upgrade.

It sounds like you’ve done a pg_dump+pg_restore based on the docs section you’ve linked to.

In that case it should be safe to completely remove the old data directory, including table spaces, as you have a full copy of the data in the data directory of the new cluster.

If you have used pg_upgrade that is not safe to do (neither are the two methods you’ve described), because some of the files are hard-linked from the old to the new cluster.

Edit: As pointed out in a comment, the latter is only true if you have used the “--link” option for pg_upgrade.