I was expecting ~ a few hours at most, not 24 hours!
Try this: create a new user with Administrator privileges. Try installing the update from that new user in Safe Mode. Make sure no leftover installers are in the Applications folder first.
If that still does not work, suggest that you boot into Recovery and run Disk First Aid. You can also reset SMC and NVRAM just in case something is hung there, but those are unlikely to help, yet no harm in trying them. (Instructions vary by Mac model, Apple has online instructions.) If still not working, download DriveDX to check physical health of the internal drive (how old is your Mac).
Finally, you can CONSIDER making at least two verified (through test restoring some folders and files) backups, preferably using different methods, such Time Machine and a "clone" utility like CCC or SuperDuper, then restore your Mac to factory settings, which entails erasing and reformatting the drive (hence the backups). Apple has instructions for doing this, they need to be carefully followed, the instructions are different for different models of laptops. Then create one new Administrator user with a name different from your previous users, say "Admin." Then apply all updates available, through 12.6. Then run Migration Assistant to migrate over only user accounts and files (no settings, no applications, nothing else) from your backup. Then install fresh only needed applications using up to date installers. This sounds somewhat involved but I have done it (due to a security update that could never complete on an older MacBook Air) and it is actually fairly straightforward, it takes an hour or two.
Alternatively, you could choose to stay with 12.5 if you wish to follow the mantra "first do no harm." Your Mac is working. But clearly something is not right because that is an update that should go routinely.