I used 1password for Android 11, but I can’t anymore.

That's a tough situation and none of the options are without cost. The factory reset was a sensible precaution before the service.

While you can try to find an APK of the last version of 1Password 8, you will still have software with a limited lifespan, feature freeze, and malware if you get it from a disreputable source. This is a poor choice.
Replacing your old, unsupported(?), Android version with an up-to-date, supported Android ROM for your device is likely the best option to keep using it safely, i.e. with both the platform and apps kept up-to-date. This comes with more advantages than disadvantages, but you should be aware of these before choosing this option.
Buying a new-to-you device is an easy option, but costs money and time to set up. Given the high cost of new devices, consider buying a recent generation used device and maybe selling your Mi 9T in a market such as Swappa. This gives you years with both up-to-date platform and apps, but how many (and how current for the platform) will depend on the device. For Android, consider an older Pixel in order to get Android updates to new versions, and feature and security updates on a predictable schedule, with a likely bonus of good support from a ROM such as GrapheneOS.

If it's any consolation, mobile devices are not designed or intended to last. If this wasn't the fist thing to stop working acceptably, then it would be the next, then the one after that. Even if you could stretch the life of the device for many more years, the technology of the rest of the world would eventually abandon you.
The closest option to being able to choose what platform to run on our perfectly good and expensive hardware is an Android ROM, but with locked boot loaders and limited hardware support, it's not like choosing an operating system to run on a PC.