My grandfather, David Fisher, has been writing an international radio program for decades called "Truth in the test tube". It's aimed at a general audience so it's not very in-depth scientifically, but the idea is to interview scientists who believe in God, just to get people to realize that they are not mutually exclusive. https://www.twr.org/judyblog/?p=2789 Even if you don't agree with those beliefs, you can't claim that religious people can't be scientists.
'Atheist' is not a prerequisite for 'rational', as much as many atheists like to pretend this is the case.
I don't personally 'get' prayer, nor do I practice it despite my Catholic upbringing, but I can see how the practice might be psychologically comforting. It's basically an acknowledgement of not having complete control or knowledge.
The thing about prayer that most people don't get is it's just a form of meditation. A lot of people think that it's just saying a bunch of words, others that it's just a conversation with God. It can be the latter and you can extract value from that if you believe but, in the sense of the former, it's never this.
If you think about repeating Hail Mary on rosary beads for n amount of times, this becomes very similar to other Eastern forms of meditation, notably the Hare Krishna mantra. The key is the clearing of the mind and focusing on the mantra.
I don't agree with many of the practices in Catholicism, having also been raised one myself, but I can certainly see the parallels in prayer with meditation as a whole. If you get meditation, prayer becomes easier to understand.