If you have frequent power outages, you should install a transfer switch like they use for a portable generator. Then plug the transfer into the Bluetti or whatever else that can make power. How many circuits would you want to backup? Can the Bluetti supply enough power?
Here is a low cost single circuit transfer switch.
When the switch is in the "LINE" position, it connects your load to the original breaker in the panel. Switch it to "GEN" and your load is fed from the plug in the box. You just use a normal extension cord to a generator outlet, or your Bluetti etc. This keeps it safe as well as legal. They make these with more circuits if you want to be able to backup other devices as well. I was using a 6 circuit box like this
at my previous house with my 5,000 watt generator. Made it very easy to switch over the refrigerator, furnace, and Dish Network.