See, it's annoying, but at least these are people who genuinely wanted kids and who take good care of them. It's especially nice to see dads fangirl over their kids, because historically it's been acceptable for dads to take a back seat. I get much more annoyed when I see people who can't pay their bills as it is and think now is a GREAT time to have another kid, or when a woman is pregnant with her fourth kid from fourth baby daddy and the first three have already been left to fend for themselves. Loved and wanted and responsibly produced kids aren't a hill I'm looking to die on.
There are better and worse ways to tell someone that they're annoying. You know them better than we do and can better predict how they'll respond, but saying something along the lines of "hey it seems like you've been really busy with your kids, totally fine, let me know when you have time to catch up" would work in a lot of cases. There's nothing wrong with telling people that you have a life outside of childcare. Of course, it's possible that you might grow apart, but that's OK if you're comfortable with it - you're not stuck in your existing social circle. Take this opportunity to go out and meet new people.