Thank you for taking the time to write this out, I probably would've been busy for a couple of hours trying to formulate my fairly similar take!
Maybe to add another aspect for - I think that the sheer ability of humans to have religious experiences in all denominations, which are often described as feelings of connectedness, does not necessarily mean that there is a higher being or reality "out there" that is being connected to in those moments.
But it does mean that our brains have religious experience as an in-built function (which, as you described, has been needlessly enshrined in religious institutions), which might mean that being able to have these experiences is an important part of being able to survive, or maybe even to thrive, as a human being, which also means as a community.
Suspending worry for the future might be a plausible function for religious experience as an evolved feature of the human mind, yes.
I would also point towards the biological fact that while the existence of a higher being, consciousness or reality, is still ineffable, even after having had an experience that felt like there might be one, there is also an empirically true, measurable interconnectedness for humans that can be tapped into.
We live, and have evolved, in and through ecosystems that highly depend on interconnected species and processes that are so complex and intricate that we are still working on fully grasping them, and still discovering new connections (unfortunately, it's becoming more and more because we have disrupted the connections by environmental damage, and the ecosystems start to fail due to that, making the connection obvious only after it ceased to exist). Connection between humans in the form of love in its many forms is also the ultimate glue that keeps societies together, and if that capacity diminishes due to circumstances, bad things tend to happen.
The myriad of connections we need to live, and to thrive and to feel like we are whole - all of this fully seen and experienced in their abstracted totality could in my eyes be one of the bases for religious experience.
And if that is true, it gives also another function - then, religious experience is the anchor and has a rebalancing function that makes sure that we don't get lost in our own heads and human constructs, and keeps reminding us that we are part of the ecosystem, too, and keeps us from using it in a self-destructive manner. There are several deeply spiritual, nature-connected societies that only became so after a local environmental crisis caused by themselves. Tapping into the interconnectedness through religious experience has helped them find another, arguably better way.
(Of course, it doesn't seem to be a hard, global fail-safe in human history, given the current state of the world, so I don't know how direct this function would be.)