The vehicle should be fine, the whole point of the EVSE is to provide a stable flow of electricity.
I had a power outage while my car was plugged in but not inside the charge window. Unbeknownst to me the EVSE (Grizzl-E classic) didn't restart properly when power returned, so my vehicle didn't charge. Resetting the circuit breaker restored the EVSE to normal and my EV was unaffected. The lesson I learned is to check on charge status after a power outage.