Update the connected field to metrics for DoT

The "connected" field for DoT is supported now. It is beneficial
to further tell the difference from sending a query via a new connection
and sending a query via an existing connection.

Bug: 144881031
Test: atest
Test: Manually added some logs to check the result
Change-Id: I3cc97660e8d5851af39d91f74d63babaa88179f8