https://www.apple.com/by/iphone-12/specs/ (12 mini)
https://support.apple.com/en-us/111873
I would recommend to return the phone and get the 13 mini which should last awhile
I upgraded an eight year old SE (first generation) to an SE3 thinking it would be the obvious choice, then promptly replaced it with the 13 mini within a week (fortunately still available at the time).
The difference is small on paper but noticable in your hands, and I honestly feel like the 13 mini is the spiritual successor to the SE series while the SE3 is a weird relative that you don't really want to have to interact with.
For some reason the slightly more boxy and grip friendly design of the SE1 and SE2 was changed in the SE3 to have the curves that were introduced in (I think?) the iPhone 6, despite the SE series having a slightly more square design up to that point. But the SE3 also inherited the lower raw technical specs that were expected from the SE series.
So somehow the 13 mini wins in terms of both form factor _and_ tech capabilities/new Apple features (such as Face ID over Touch ID).
Sometimes you don't quite catch it at the right angle (and sometimes it sees you when you're not even looking), and other times you just don't quite have enough fave visible for it to work (for me usually when I'm doomscrolling in bed with my face squished into a pillow, so maybe that's a sign).
I'd pay about the same (or maybe even exactly the same, but feel a little annoyed about it) for a small Apple phone with the same camera as the expensive big models.
Also I wouldn't choose one with a lightning connector, better with a USB-C (or A) female port, so I could also use it for some other devices too if necessary.