I really appreciate a chance to discuss this with a fellow dad. A lot of these things quickly touch on what we value and believe, rather than what we can prove.
So for example - even back when I was an atheist (I was born in the USSR) - I had a feeling that life had a purpose, there was a potential to live up to, there was meaning and reason beyond just me. In a way that's a religiously originated belief that happened to "survive" for a while unrooted from religion, but clearly originated from it.
Now that I've come back to religion, one lens on it is that it's simply the necessary context in which meaning and purpose can exist. For example, if as an atheist I encounter another atheist who is a nihilist or hedonist (as proxy for not having anything greater than themselves) I have no logical foundation from which to say there's more to life than that. But as a religious person talking to another religious person, establishing that baseline is trivial - that's not where the effort goes.
For a belief to be "outdated" requires something updated that works better. One obviously true attribute of atheism is that it doesn't enable its adherents to have enough kids - so from a purely Darwinian metric it obviously doesn't work. It's a hard sell to say "here's a better belief, sure it'll drive you into an evolutionary dead end but... uhh yeah it's better"
Congrats on your two girls and while I also want my kids (2 boys and 1 girl) to have maximal autonomy, I have a great role to play in shaping their thinking and values. For example - whether I live in a neighborhood with a lot of families of in a city filled primarily with spinsters, whether I convey my own values around children or not, whether I encourage a social group that is positive about parenthood vs one that sees kids as undesired burdens, these are all things within my control. And my personal belief is that my kids will be happiest and have the greatest meaning in life if they - like me and my wife - love life, and want to pass it on, and to use our children as a way to contribute positively to the future. So yes I want to pass on these values, yes religion helps that, and also - if we don't do that - the future will simply be inherited by the kids of parents who do. It's not about sustaining fertility rate in some mechanistic sense, it's about a dropping rate being a numeric symptom of a problem I don't want my kids to suffer from if I can help it.
I agree with the desire to not move your kids "online" but I don't think green spaces are gonna do that for you, as plenty of kids live near the park but never look up from their phone. I recently realized that a religious lifestyle "forces" more in person interaction, as I alluded to in my original comment here. For example, it's my religious friends that attend services together - physically, that go to each others houses for lifecycle events, that study as a community.