I just now registered with MN (after years of lurking) to add a message here because yes OP, that did happen to me, almost exactly, in 2015. He already had a son with an ex. I'd been on my own for years and had become very good at solitude. Neither of us had intended to become so deeply involved but we were such a good match on the surface like you, "amazing chemistry, never a fight, always laughter" that we grew very close despite ourselves. Like you, I couldn't blame him for what he felt: he had a deep, primitive longing for more kids. But I'll be honest, I felt devastated when he backed out.
You asked how to cope. I don't know. It was hard. I just did the usual things: kept busy, exercised a lot, visited distant friends and family. It took a while but eventually I started to feel a little better. He and I had been friends originally, and found that after some time we were able to remain so. And then to my surprise I connected with someone else. The new man's kids are grown, and he's a much better partner for me in every way.
I say this without even a whiff of schadenfreude but four years later I'm happily engaged and the man who left me still hasn't found anyone to have those kids with.
It'll hurt for a while but you'll be all right. Message me directly if you like.