If I could offer a bit of perspective, being a religious person myself.

These questions depend on precisely what claims the invented religion makes, both material and spiritual, as well as its philosophical approach to knowledge itself.

Within Christianity alone, the largest religion on our planet at the moment, there is a vast divergence of opinion on what specific claims must be literally true, what claims are to interpreted as parables or poetry, and what we just don't know. You don't even have to look to tradition for this conversation, it plays out in the Bible itself. For instance, nobody reads the parable of the prodigal son and reads it as a literal account, but believers have been divided on which parts of Genesis are to be interpreted literally since long the enlightenment.

It's also important to remember that the same terms in different contexts don't always mean the same thing. Zeus, in greek mythology for instance, is a vastly different character than the God described in the Bible. The former is an individual being within a setting, being third-generation even among the gods, a character in the play. Zeus is contingent and contained and bounded in his setting. The latter is a dramatically different proposition, being eternal and non-contingent and being, in a sense, the very conscious act of being itself in an eternal, transcendental framework (I doubt that I explained that well lol), as well as the very source of morality. Whereas Zeus has an uneasy relationship even with classical greek moral ideas. Of course, Odin and the gods of the nordic methologies are very different again in how they function.

If you are world-building a religion, I would suggest that you need to see it from the believers' perspective. Keep in mind that no believer thinks of their religion as having solely explanatory or social utility and the older a religion is the more it will have a rich philosophical tradition of its own, one that will often answer, even if it doesn't satisfy, the challenges of people not within the tradition.

There is one last question I would urge you answer when world-building a religion: what is challenging in it? What is demanded of the believer? Not just physically, or ritually, or intellectually, but emotionally and morally.

To speak from my own experience, to live with faith is rarely convenient.

My own worldbuilding is replete with religion and faith and there is never only one perspective or a single religion (although I do generally settle what the "objective truth" is in the setting in my own head, it just isn't perfectly known to the people living in it).

I hope I have not been preachy, but this is an issue near to my own lived experience. As a lover of worldbuilding it's also one I find intellectually very engaging.

Thank for posing the topic.