If it's not mapped as a hotkey, either globally or as a profile override, the only option that produce a "Listening Resumed" log entry but no other entries is the aforementioned command using the "Ignore an Unrecognized Word or Phrase" action.
However, all options produce either a sound, or a sound and a log entry.
There is no method of resuming listening that produces a log entry, but no sound, that I could find.