I noticed, and im sure many others did too, that the end of season 3, ted comes home, henry comes out of the house, greets him, and michelle is at the door. Henry ushers ted in, and shortly after they are at a soccer game with henry, where michelle says " come on boys", cheering both on? Are they back together?
Yes, I’ve wondered about that too. It is a bit of a mystery, why it took so long into their marriage for them to have Henry. I saw a copy of the pilot script online, and in it Ted is described as 40 years old, and Henry as 10. So that would mean he and Michelle had Henry aged about 30, which would be more understandable - they got together in college, established careers, bought a house, then had a child (then we might wonder why they had only one, but still).
My guess is that the character ages were largely because of practical/production reasons - I think the Ted Lasso script was probably written when Jason Sudeikis was 40 or close to, but not shot until he was 45. I’m not sure why Henry got aged down except that younger kids are kind of cuter.
In-universe, I think your theory about fertility issues is a good one. My other head-cannon was that maybe Ted was a bit fearful of parenthood and kept putting it off, because of what happened to his dad.