But I'm aiming for something that's the same size as the PCB-mounted Ethernet jack itself.
That's probably too small, unless you forgo
compliant ethernet transformers and
compliant PoE. That Waveshare item you link is about as tiny as I would expect things to go.
Where do you want to mount this? Are you imagining installing it in a wallplate (lots of space) or in a rackmount keystone/module (tiny)?
I assume I can't just suggest a Wifi solution like an ESP32? Wifi is cheaper and smaller than compliant ethernet, but BYO power.
EDIT: Your linked Waveshare board is smaller.
An Orange Pi Zero is bigger than what you want and is over-powered, but IIRC can support passive PoE with a few solder jumpers. If Element14 has stock then a
FIREWALK might do the job.