Currently execution time for the replicated query is not limited in any clear way. On primary node we can use max_statement_time, but this value is neither passed to slave nor enforced for SQL thread when it's set locally. So, there is no way to "control" replication delay and just stop with error when it's too big already.

I think option to stop with error after specific timeout (that may be different than local max_statement_time or primary's max_statement_time) would be useful for replication setups.