Looking at the circuit and photos, here's my guess:
Power lines L and N come in the top left, then some protection and line filtering is there, which then goes to a bridge rectifier to generate mains rectified DC voltage across C1. If C1 is big (large capacitance), then this is not a UPF circuit since then the frontend is practically just a rectifier.
T1 looks to be a flyback inductor, winding 4-6 is the primary - its got a snubber across it. Winding 1-2 is probably a sense winding, it is used to detect amount of flux in the core. It also seems to be generating some sort of bootstrap voltage across C31.
Winding 7-8-9-10-11 is the secondary - the turns have been designed to give 3.3V and 24V. IC1 provides the isolated feedback loop.
I can't see R6 and C34 in your photos, but my guess is that they are there for mains voltage sensing and/or powering the chip at startup.
So: you need to search for
- a switch mode power supply controller chip, 8 pins
- Feedback on pin 2
- Overcurrent detection on pin 3
- Ground on pin4
- Capable of driving MOSFET, gate o/p on pin 5
- Oscillator on pin 6
- Pin 7 unknown
- Pin 8 maybe supply?
Since I happen to have nothing better to do at the moment, I did a little digging on Digikey with the above constraints and the first one that popped out is UCC28600.
Having worked in this area briefly I know there are dozens of pin-compatible replacements from a variety of manufacturers, so finding the matching package markings might be near impossible.
However, since your interest is presumably to just get your printer working, you could just desolder the transformer o/p and patch in 24V and 3.3V from a different power supply.