I just tested logical replication both ways between current master and v14 branch tip, and in either case the publishing server stops pretty much instantaneously after "pg_ctl stop -m fast". So I don't see anything broken about our code, and I remain of the opinion that Qlik is probably at fault.
Ok, yeah. Looking more closely the reconnection attempt in the log doesn't look related to this so those hung connections are not playing nicely when told to go away. Which indeed in fast mode we have to rely upon.