The problem is that $dbh->dbix_threaded_start_prepare won't return the statement object handle, so $sth ends up being empty.

I agree that the documentation is very confusing.

The $dbh->dbix_threaded_start_* calls don't return handles, they return immediately with IDs.

You then have call $rc = $h->dbix_threaded_wait( $id ); to wait for the thing you started to complete.

So, to asynchonously prepare a statement, you'd do (something like; untested):

my $prepID = $dbh->dbix_threaded_start_prepare( $sql, ... );
...
## you can do other stuff here
...
my $sth = $dbh->dbix_threaded_wait($id);
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But you don't need to use the asynchronous calls for everything. You could just use the normal dbi calls for some things.