statement_timeout has no effect if sync standby is unavailable

I am writing a monitoring tool to find if the database is hung.

One of the scenarios is to stop the standby but keep 'synchronous_standby_names=standby1' and 'synchronous_commit=remote_apply' unchanged on primary.

This way the DML queries on primary will be hung. I tried to use 'statement_timeout=5s' to timeout the query but it does not work.

Is there another way to timeout query and report an error ? and why is statement_timeout not working?

Thanks,

Nikhil