AudioService: log routing cache clear time, cache sync

Use lock for cache and clear time from creation to use
and logging.

Bug: 266211560
Test: adb shell dumpsys audio | grep "AudioSystemAdapter" -A 2
Change-Id: I3cc82ef8287c74997b48eb5c1f5713154ffbadd2
Merged-In: I3cc82ef8287c74997b48eb5c1f5713154ffbadd2