It is not the moisture you need to worry about in a power outage. For a few hours you can manually keep media moist and tank surfaces roiled with battery powered air pumps. What you cannot do is keep tanks cool in very hot weather or warm in freezing temps without heating or cooling the entire residence. The bacteria will also die if they freeze or get much above 100F for any amount of time.
We were able to afford a whole house back-up generator. As long as this does not fail, power outages do not bother us. I should mention that I have several pricey pleco species I breed and it is not uncommon for me to have many $10k of fish in my tanks. It took me about 15 years and a lot of luck to reach that point. As well as the fish, we were caring for my mom who had dementia and who was entering her 90s. She could not handle a loss of power during extreme temperatures either.
In the years since we put in the generator we have had two power outages of 13 days each. The hurricanes of 2011 and 2012 came up the east coast and hit us. We are about 30 miles NNE of NYC as the crow flies. in 2019 we had one of about 3 days.
The greatest danger from power outages is not dealing with manually keeping media damp or using battery powered air pumps to keep the surface agitated for oxygen for a few hours. It is from the temps if they are near freezing or lower or heating up to 100F for any amount of time. Both of these things will kill most fish and the bacteria cannot be frozen or kept above 100F. A few hours in such conditions one can handle, an extended period is another story.
I am lucky that we could afford whole house power back-up. It is not cheap. Mom has since passed but my rare pleco breeding efforts have resulted in my having fish worth a ton of money in my tanks, I work with zebra plecos, L236 (including super whites) and L173. I have several clown loaches with me since 2003 and which are my favorite fish. They are almost a foot long now. They are my favorite fish.