Your bathroom receptacles are protected by a GFCI safety mechanism. You can confirm by noticing if the receptacle has two small buttons usually stamped with "Test" and "Reset".
If the smart plug had a malfunction due to humidity (unlikely), the GFCI receptacle it's plugged into would instantly cut power.
You can toss a toaster in your bathtub as long as it's plugged into a GFCI and 99.99999% chance you would be totally fine. Don't try this at home.