Concerning your first issue:
Do you have the ap-poe-power-optimization provisioning option enabled for this AP? That will reduce the amount of power the AP claims via LLDP, but will disable both USB and PSE. USB can be overruled, but PSE will always be off in this case.
If you did not enable this option (default), enabling PSE still requires the AP itself to be powered by DC or an 802.3at compliant (class 4) POE source.
While it is true that the typical consumption of an AP-303H is much lower (worst case idle power consumption is <5W), the power budget needs to be based on worst-case consumption in fully active mode, which is 9.7W.
In addition, when we enable PSE, that could result in a maximum of 15.4W being drawn from the ethernet power. As a result, we need the full 25.5W 802.3at POE budget to enable this capability.
I'm actually not sure by you claim to "only" need 21W for this. At the switch side, max 802.3at budget would translate to 30W.