Right, let's leave the fertility issues to one side for a second and pretend it's a standard situation.
My actual best best friend had a baby nearly two weeks ago, I went to see them today for the first time. Yes, we have been whatsapping, but not everyday as I dont want to disturb her or the baby, I'd feel bad if her reaction was "gawd, I'd just got to sleep and my flipping phone vibrating across the sodding table woke me/the baby up - I/we only got three hours last night" (yes, I know she wouldn't actually put that into a text - but it definitely would be a lot of people's reaction if it happened!) she has a shit ton of people texting her anyway, that was apparent when I was there.
I don't want to be the one pestering her.
And honestly, I have replied with a simple "aw, that's adorable xx" or similar because I have a life too and sometimes being able to write a longer text is something I couldn't provide at that precise second.
She also has her DH at home, me and him get on really well but that doesn't mean I want to go playing gooseberry to their new little family.
She has her mother there a lot too, again - me and her = house on fire, but three's a crowd?? I wouldn't have liked to have three/four people in my house at once, tbh.
Also, from my own personal experience of new babyhood is that a bit of space is nice, I loathed the doorbell ringing just as I had managed to latch the baby on properly then being expected to brew up and scootch over to let them sit down when I simply felt like shit. so now I am very respectful of space when new babies are in the picture. I actually wasn't even going to go til next week .... !
Right, now fertility issues! We struggled to conceive first time and during that time another girl I knew got pregnant, not to mention all the preggos that you see day to day anyway.
It was simply hell.
She was a very laid back sort of person and smoked and drank (not to excess, but still..) I just wanted to slap her and scream 'why her and not me?' We were comfortable and married, I'd already given up drinking for months and she was feckless and flippant and gambling with her baby's health!! I was properly RED MIST angry at her for a very long time - well after my own baby came along even! It turned out later that she had MH problems that I was unaware of at the time and now she is very remorseful about it all.
Of course I know it's not anywhere near the same as your circumstances but I know I'll never judge anyone about the way they handle their infertility and other peoples babies ever again.