That UPS eventually died, and I'm not sure if it was because it was hooked up to a larger battery than it was designed for, but it's still only 12 volts so I don't think the electronics would notice. What they may notice is extended run-time in the event of a power failure.

It was a crude mod. Take the cover off and remove the existing little security alarm battery, use tin snips to cut a hole in the side of the metal UPS cover (this was challenging, it was relatively thick metal, I'd recommend using an angle grinder in an appropriately safe environment far away from the internals of the UPS), and feed the battery cables out through the hole. I probably got some additional cables with appropriately sized terminations to effectively extend the short existing ones (since they were only designed to be used within the device). And then connect it up to a car battery.

Cover any exposed metal on the connectors with that shrink rubber tubing or electrical tape. Be very careful with exposed metal around it anywhere, especially touching the RED POSITIVE pole of the battery. Get a battery box - I got one for the big-ass AGM battery.

Test it out on a laptop that's had it's battery removed or disconnected that, just in case, you don't care too much about losing.

Get a battery charger that can revive a flat battery, and do a full refresh/renew charge on the car battery once a year or after it's had to push through a power outage that may have used more than a few percent of its capacity.

Personally, I think it's safer a less hassle to go for a LiFePo4 (LFP) Power Station style device that has UPS capabilities. LFP batteries have 3,000-ish cycle lifetimes, which could be nearly ten years with daily use.