I have only the 5V version of 28BYJ-48.
I read somewhere that even that version can be powered with 12V.
Since you said powering your 12V stepper with 5V is possible, it is likely to turn a bit slower than powerded with 12V.
In general I read that it is dangerous to drive the stepper from Arduino 5V rail.
I have several Arduino Unos and take the risk until really something breaks.
I do drive 2 such steppers from single Uno 5V and have not seen any issues sofar.
First I did control the stepper PT camera system from Arduino.
Lately I changed to Raspberry Pi (for real time automatic camera centering).
I did not want to risk my PIs, so I still use the Uno, but just as 5V power supply.
The bottom stepper has to turn top stepper and 70mm lens, both together 55.5g weight:
https://forum.arduino.cc/index.php?topic=647703.msg4369656#msg4369656