Add logging for private DNS probes

Also includes registering validation events as metrics.

Bug: b/111596247
Test: as follows:
  - Built, flashed, booted
  - Configured strict mode
  - Connected to working WiFi, then WiFi with no connectivity
  - Changed private DNS server to invalid value
  - Re-connected to working WiFi
  - adb shell dumpsys connectivity has PROBE_PRIVDNS events with success
    and failures of the probe

Change-Id: I2691dffd60593fdeaedd22f7ec04a76029f6297c