I keep pointing out that the sun's motion around the Milky Way is not an "orbit" in the sense that we usually think of it. It is not even a closed curve. Orbits in a central potential like the solar system are closed curves, but orbits in a potential well like the Milky Way's are typically not. Even if the Milky Way's potential were static in time the orbit would not be a closed curve, and it is definitely not static in time. So it is best to think of the sun's motion as an approximate orbit, where each path around the Milky Way is a different curve.
No argument there - I agree that the sun won’t return to the same place in another 230 million years or so for the reasons you have noted. “Approximate orbit” is a more accurate term than just “orbit.” In a sense though, the earth doesn’t return to the same spot either after one trip around the sun since it is moving through both space and time.
I have amended my diagram so that it doesn't show the sun’s orbit as a closed curve.
But the original intent in my previous post was to point out that the sun moves in unison with our rotating galaxy - not against it, and that its up and down motion is relatively very small.