Ethernet PoE with the Ethernet expansion
is PoE possible at all using the Omega2 and Ethernet expansions? This is a perfect device to power over PoE when possible and the project needs an ethernet expansion!
You have to make sure the Ethernet magnetics is the type that supports PoE (i.e., the windings can handle the current supplied from upstream.)
What's the component part number printed on that Ethernet magnetics?
(In one of the pic it showed M3066ANL. That type seems to be not specifically designed for PoE applications.)
If it's about 802.3af PoE compliant approach...
Above statement is for DIY modification on existing Ethernet dock (e.g., adding a RT9400 module and a large capacitor.)
This does not preclude a new design with factory built-in PoE capability nor
a separate PoE adapter module in front of the Ethernet dock.
There is also an ad-hoc, non-standard approach using pairs 4+5 and 7+8.
In all cases, the PoE supply voltage needs to be pretty high such that the instantaneous power demand (over the long and thin Ethernet cable ) from O2 will be less susceptible to cause the power-dip/brown-out condition and then hang the O2.