How do I determine the current "idle timeout" value for PostgreSQL?
Before 9.6, no such timeout exists in PostgreSQL. Thereafter, it only exists if you are idle in the middle of a transaction.

show idle_in_transaction_session_timeout;


Note however that any router, gateway, or firewall between you and the server can nuke your connection at any time it chooses.  TPC keepalives may or may not dissuade them.  PostgreSQL can't offer much insight into what your networking equipment does.