A good rule of thumb when asking a question about science and nature is, I believe, the following:
Ask yourself First or something really is so, before you wonder why .
Polaris actually moves .Among other things due to the annual tour of the Earth around the sun.This movement — which is called parallax — is, however, so small that we need a very precise instrument to measure it. The reason the movement is so small has to do with the enormous distances in space.
Outside the yearly parallax, there are two more effects that make the spot of Polaris on the outcrop not static. I’ll go deeper into that below.
The orbit of the Earth around the sun has a diameter of approximately 300 million kilometers.This is a huge distance in our experience, but the distance to even the nearest stars is much bigger; Those are in the order of tens of thousands of times as far away as the size of the Earth’s orbit. Just as you can quickly move the roadside of the road from a moving car, the trees on the horizon are much slower, and the moon seems to stand still in the sky, in the universe also that things that are far away seem to be almost silent because your own movement is once R Elative is small. An interesting fact is that the parallax of stars can therefore be used to estimate their distance. The larger the ‘ circle ‘ that the star seems to make in relation to the background as a result of the yearly circle around the sun of the Earth, the closer the star.
Here you can find more information about measuring distances in the universe: Astronomical Distance measurement-Wikipedia
Effect 2: The Own movement of stars:
You rightly suggest in your question that the movement of the solar system in its orbit around the center of the Milky Way should also ensure a movement of Polaris (and of all other stars).That’s right: all the stars we can see at night with the naked eye, have their own orbit in the galaxy, and all the stars are therefore moving relative to each other. But because the turnover of a star is in the order of hundreds of millions of years, these relative movements are so slow that we cannot easily perceive them in most of the stars. It takes tens of thousands to hundreds of thousands of years before you would see clear differences to the shapes of the constellations with the naked eye. The starry sky therefore seems static.
Here more information about the own movement of stars: Own movement-Wikipedia
Effect 3: The precession of the Earth axis:
Finally, you may find it interesting to know that the earth axis is slowly changing angle and direction.This effect is called precession and causes the spot of the sky poles to slowly shift. As a result of that precession, Polaris is no longer a polar star over a few thousand years, but points the extension of the earth’s axis to another star. The precession of the earth has a period of approximately 26,000 years which means that Polaris will again be temporarily our Arctic star.