Asking about the effect of enjambment in this poem, is asking how it is different than this:
so much depends upon a red wheelbarrow glazed with rain water beside the white chickens.
The same poem, with all the extra line-breaks and spaces taken out. It ends up being just a sentence. Much less poetic.
How do we read this sentence differently than the poem? Mainly, we read it faster. Line-breaks create a stopping-point. If reading silently, it takes time for the eye to adjust down to the next line. If reading out loud, the end of a line is usually given a short pause. But when all the words are in a single free-flowing line (there aren't e.g. commas to induce a pause) then we read it faster.
Okay, so the effect of enjambment is to slow down the reader. What does that add to the poem?
The poem is in line with Imagist ideas; it is concerned with carefully and precisely painting an image. Indeed, six of eight lines, and three of four verses, are entirely devoted to this image. Slowing down the reader forces them to give more time to considering the scene.
As your eye slides slowly from line to line, your brain has time to carefully consider the image and build a precise picture of it in your head. It is precisely the languid movement of the poem, caused by enjambment, that allows you to take - forces you to take - ample time to think about the image.
Thus we can say that the effect of enjambment in this poem is to slow down the reader, in order to better draw an image.
I will now consider authorial intent, since that was explicitly asked for in the question.
Williams wrote, as quoted from Wikipedia (which is itself quoting from other sources):
["The Red Wheelbarrow"] sprang from affection for an old Negro named Marshall... In his back yard I saw the red wheelbarrow surrounded by the white chickens. I suppose my affection for the old man somehow got into the writing.
Williams saw a red wheelbarrow which was surrounded by white chickens. This image moved him so much that he wrote it into a poem, to share it with the world. He wanted his reader to experience the red wheelbarrow next to the white chickens along with him, and take in the scene with the same affection that he felt. Thus he slows the reader down by using enjambment, to force slower and deeper consideration of the picture he paints.