Previously, the URI template handler installed by the client metrics
interceptor would always capture the URI template and push it onto the
deque, irrespective of whether auto timing was enabled. When
auto-timing is disabled the deque is never polled so this led to its
unrestricted growth.

This commit updates the URI template handler so that a URI template is
only pushed onto the deque when the auto timing configuration enables
the interceptor.

Fixes gh-26915