Electrons are fermions.
I am therefore comfortable saying that electrons are matter.
I don't know why you say that electrons are "not particles" in QFT. Sure, there's an electron field, and electrons are just, like, excitations in that field. There's also a quark field. What of it? If you are saying "because everything is fields, there are therefore no particles, and therefore no matter", you are using the word "matter" in a silly way.
Also, isn't a "particle" just a representation of a compact Lie group? What's the problem?
(edit : though, I admit that I'd be a little hesitant about calling a massless fermion "matter". But, seeing as there are no known massless fermions, meh.)
I'm not sure this is resolved. see: https://en.wikipedia.org/wiki/Quantum_electrodynamics#Conclu...
> Or is it that energy can have mass prior to being converted under some conditions?
Using https://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalenc... you can (theoretically) convert between energy and mass, and then measure everything as https://en.wikipedia.org/wiki/Electronvolt. I have yet to see anything create protons from energy, so I am hesitant to do this.
Won't a proton/antiproton annihilation also create two photons? If so, wouldn't that also work in reverse?
I expect it would make a lot more than just two photons. See: https://en.wikipedia.org/wiki/Annihilation#Proton%E2%80%93an...
> If so, wouldn't that also work in reverse?
It would have to be demonstrated.