My wife definitely got to what you're describing as the "awww, baby" stage (what you say *you* feel) after starting HRT, but nothing approaching that kind of baby craving. Which is good, because we don't have kids, I'm likely within sight of the end of my fertile lifespan and she's post-GRS with nothing banked, and I'm pretty solidly not interested myself at this point even if we could manage to convince someone to let us adopt. 🙂 She does occasionally say it's making her sad to know she'd never be able to get pregnant, but she doesn't actually want to *have* a baby, if that makes sense.
This also lessened with time - she's been on HRT about five years now - but then again, I dunno how much comparison there is to your situation. You have my sympathy... assuming that you're kind of wishing this phase would pass, that is.