I find it also hard to read it that way when I look at that "Price in February -> Price in April" annotation: if those two points on the y-axis mark points in time, then so do the correlating points on the x-axis. I can only read that as "from February to April, the demand went up while the prices went down".
I agree with you that price should be on the X axis, and drawing the two supply lines in the same diagram is at least somewhat problematic.
What economists posit[0] is that at any point in time, there are demand and supply curves. They answer the question of who is willing to sell or buy how much given a price? (Quantity is the dependent, so should be the Y axis!)
And they argue that the microarchitecture of the particular market causes price and quantity to converge to where these lines intersect.
And then factors external to the market can change the supply/demand curves. The February diagram looks different from the April diagram. They are conceptually separate diagrams. Combining them into a single diagram in a coherent way would lead to something 3D, which is hard to draw and think about, so economists have the convention of drawing it all in a single diagram anyway.
None of this is correct, by the way, but it's sometimes a useful model.
[0] Outside of literal markets with order books, supply and demand curves don't really exist. And in those markets, their dynamics are different.
Since the graph is without units, the only relevant of their positions are the signs of the slopes, and that you need a higher price to supply oil at any given quantity (hence the Straight closed" line being higher on the graph).