I’m having some undervoltage problems at home: the power is supposed to be 110V, but it constantly drops to 90V. If I run my Bluetti in UPS mode, could these fluctuations damage the unit? Also, does it have internal protection for this kind of voltage drop?
Independently of the Bluetti unit you are using, voltage drops on the AC side are not supposed to damage the unit.
UPS mode will intervene to make sure, if power is within limits and battery charged enough, that your output side will continue to provide power.