Because it belongs to the power stage, a PoE transformer is chosen against the converter: the input range behind the PD controller, output voltage and current, switching frequency, topology and the isolation the safety case requires. The PoE class sets the budget, but two PDs of the same class can need different DC-DC transformer designs.
Most low and mid-power PD supplies use a flyback transformer, while some higher-power 802.3bt designs move to an active clamp forward converter. Confirm the intended topology in the datasheet before treating a part as a flyback transformer for PoE.