Then a simple cable that plugs into your XLR powerchair port at night means that your bed will work great even when the power goes off.
You need XLR, 3A fuse, a single Diode in the cable so that the beds power supply doesent try to charge the chair.
Totally simple, easy to make, cheap. And reliable with nothing else required.
You can do the exact same thing with 7 cells series connected (18650 cells). But quality 3Ah LG or other known brand like Samsung, Panasonic. That will work for days. Charge once every 6 months to be sure. Use a simple ni-cad - lithium 18650 cell charger. Loads on ebay.
Or
https://www.aliexpress.com/item/1005005 ... vfkRbYW4R0No chair needed.