I have always thought of religion and science as two sides of the same coin.

I think this is a reflection of their shared phylogenetic history. Religion, science, and philosophy probably emerged from the same ancient thought tradition.

However, it seems to me that as long as there are questions that have yet to be solved by science, humanity will find a use for religion.

I'm with you on this, but only if we use the word religion in the very limited sense of describing "something supernatural". I could see people in still saying "well I think God is like an energy that fills the Universe" or say "well God is just the laws of physics", etc. But a purposeful, anthropomorphized, creator God is on the way out.

As soon as the entire universe has unfolded before our eyes, and once science has solved everything, religion disappears. But so does the need for science. I don't believe we will ever come to this point because surely the Universe extends beyond what we currently perceive as possible, and its complexities may develop infinity.

Yes, agreed. I think problems and mysteries are an inherent function of living in a Universe governed by entropy. The universe is knowable, but we will never "know all the things".

I always considered the greatest irony to be if there is a god, that they are a scientist who simply discovered a way to program or create a universe.

Some physicists consider this a likely scenario.