First issue: Your might need to redefine your definition of conjugated. "3 or more overlapping P orbitals" might be a better definition than "single bond/double bond/single bond." Read about allyl cation, anion and radical. These three species contain the smallest unit of conjugation. All three species are stabilized by this conjugation.
By my definition of conjugation, a molecule like butadiene is an
example of conjugation, but not the prototype. Butadiene has 4 overlapping P orbitals, one more than it is necessary.
I have sometimes seen conjugated defined as "single/double/single etc." but I think it's probably better to define it in terms of overlapping P orbitals because this better describes the true reason for the stabilizing effect.
By any definition of the word, a phenyl group always contains a conjugated system. So you're not going crazy when you notice that!
As for my words about resonance structures, here is a link to a picture that might better explain what I was trying to say:
https://imgur.com/a/4536lQlDrawing resonance structures is not the most rigorous explanation. The best thing to do would be to consider molecular orbital diagrams. But that's not my forte.
Edit: I should add also your are correct that the upper nitrogen is electron donating. So it pushes electrons down toward the radical nitrogen. Radicals in general are usually stabilized by both electron donating and withdrawing groups. But I think conjugation with benzene has a much stronger effect.