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Small ones aren’t large at all anymore.. battery tech improved significantly.. $59.95 for roughly the capacity being discussed here.. (small computer, short bridge time) Integrated in an outlet extension with surge protector.. should suffice for a laptop/router or a regular computer etc 425VA/260W Standby Uninterruptible Power Supply (UPS): Uses simulated sine wave output to provide battery backup power and to safeguard home office, home entertainment including computers, gaming consoles, and broadband routers https://a.co/d/090l855X — But integrating it into the device is stupid for other reasons. Power is out, your computer stays on. But the WiFi is out, the screen dark, printer etc off too.. You need more than just computer powered, at the very least the screen.. considering cloud conouting etc nowadays, WiFi might be essential too..
You could get a UPS. We use them at work and I have them in my rack at home. When power goes out and it's on battery power, it beeps incessantly until you do something about it or power is restored. This one is like $60 and will beep every 30 seconds it's on battery. Also a bonus that it will keep some of your devices going for a little while longer.
You bought a 12V DC UPS. It's meant to replace the power adapter that came with your device. It should've come with some cords with barrel connectors on the end, and it looks like it's the right size for the XB8. However, the XB8 requires 4.6A and that UPS can only put out a max of 2A. It doesn't have enough power to handle the XB8. All you need is a simple 120V AC UPS. It has standard receptacles on it, which accept standard plugs. https://www.amazon.com/dp/B07GZR981Y/ is one example. You just plug your device into the UPS instead of the wall, and plug the UPS into the wall.