Logical Replication to Older Version

We recently upgraded from v9.6 to v13 but are seeing some problems. It's on
AWS Aurora, so I won't ask to diagnose a heavily altered version. We're
hoping for better results with v12, but when we set up logical replication
from v13 to v12, while the initial data snapshot copies the data,
pg_stat_replication remains empty.

There are no v13-specific features or idioms in use in the databases. As a
sanity check, should it be possible to set up logical replication from a
newer version of PostgreSQL to an older version? Has this scenario been
tested? Has the logical replication protocol changed between versions?

Thanks in advance,

Miles Elam