What we see as sunset is that eventually the earth sinking?

Answer

We see the Sun set because we are standing on the Earth, and it revolves around its axis.

I make it clear on the drawing. It shows the Earth and the Sun three times. The Earth is on the left, you are the black dot. Everything above your horizon (the oblique line) is visible to you, the gray part below is not visible to you because it is below your horizon. The arrow on the Earth shows the direction in which it rotates on its axis.

1) at the top, the Sun is still 45° above your horizon.

2) below, a few hours later, the Earth has rotated a little further on its axis and the Sun is only a few degrees above the horizon.

3) a few more hours later the Earth has rotated even further (and your horizon naturally rotates with it) which makes the Sun now sink below your horizon.

So when we watch the Sun go down, we actually see the effect of the Earth spinning on its axis.