The new spiritual paradigm
Nicely stated division between the religious and spiritual world. While this is something that you discover in yourself it is also important to understand that the religious world is an old approach to spirituality that for many reasons is fading away. While there were serious investigations and lessons on spirituality back to the earliest origins of Buddhism and others this is predominantly a conflict between old paradigms and new paradigms.
We are living in a great transitional period of paradigmatic change driven by population secondarily and technology primarily. Paradigms are large metaphorical sets that assist in visualizing related aspects of the universe in which we live. That is exactly what you describe in discovering that the religious world is no longer comfortable and a new visualization of personalized links to the universe and other living things, a spiritual world, seems spontaneous and natural.
The new paradigm replaces the old. But the reality is that the old still survives for those that have not discovered the new or who are not yet comfortable with it. But these are changes that scale to dominance very quickly once a threshold is past. That is why this is seen, primarily, as a generational change. The current generations are in the new spiritual world paradigm.
Another note to consider is that the new spiritual paradigm is atheist in form. While you can call the spiritual universe ‘god’ or the unity of us with the universe ‘god’ if you like those are not traditional, religious deities. That’s an area of conflict with those still in the old religious world. The only old religion that is atheist (and spiritual) at its origin is Buddhism and most people, including most traditional Buddhists, don’t realize that. Gautama was not divine although he was made into a divinity by forms of Buddhist religion because that was what was expected and wanted for two millennium.
And so, I believe, I’ve answered your question.