Help me identify this small transformer
That is the high frequency power transformer in the switching power supply.  It is probably intended to have up to 400 V on the primary, chopped at a few 100 kHz.

Since this power supply works down to 100 VAC input, and it is too small to probably have PFC, it is probably intended to produce a bit more than 5 V square wave out with a 140 V at maybe 200 kHz square wave in.

Transformers are proportional, so you can feed it a much lower square wave as input and see what comes out.  The winding with the highest DC resistance will be the primary.  Put whatever your function generator can do at maybe 200 kHz in, and see what comes out of the other windings.

You're not going to find a datasheet, since this is probably a custom transformer made to whatever spec saves the most pennies for this mass-produced power supply.  When you buy 1M transformers a year in lots of 100k, you can get exactly what you want at very low prices, especially when cost is the overriding concern, and quality only means it doesn't catch fire or die within a year.