The changing nature of God

I'll caveat this by starting with the fact that I'm not a Christian, but I've become increasingly interested in Christianity because of its historical and cultural relevance. I'm not here to try to convince anyone of anything, nor to debate anyone's beliefs - just to get a sense of what a cross-section of Christians think and believe, since I think this sub is a good sample and likely has some diversity of opinion.

There are plenty of threads about differences in the behavior of God in the Old vs. New Testaments, typically explained by cultural influence at the time of authorship and the fulfillment of the old covenant and arrival of the new. I'm more interested in your opinions on the differing nature of God throughout the Bible, and how you reconcile this with the concept of an unchanging eternal God.

For example, in some places (particularly the Old Testament) God has very human-like qualities. In many stories he becomes angry or jealous, both of which are very human emotional responses which would be fundamentally incompatible with an all-knowing being. After the flood, He places the rainbow in the sky as a reminder to Himself. He often sends heavenly beings to Earth to gather information for him. Plenty of other examples, but the idea is this: the Old Testament God is portrayed as having many very human-like limitations.

In other parts (particularly the New Testament), he's portrayed as an almost Platonic being (omniscient, omnipresent, omni-etc...), which is closer to the modern concept of God. This is generally how God is explained, and how he was explained to me growing up in Christianity.

So my question is: how do you reconcile this? Does God's nature evolve with time? Are the limitations a reflection of the Bible's human authors' and editors' limitations in understanding God? Some other explanation?