I think (but don't know, I'm not an astronomer) the ancient Greeks and Egyptians saw a different sky than we do because of the orbit around the center of the galaxy. I'd have to look it up, but that might have changed how constellations looked.
I do know in the far future (like several billion years), stars will be farther apart in the sky and eventually as the universe expands, you won't see anything except pitch black. It's spooky stuff ._.
The more noticeable cause of the sky looking different for the ancient Greeks would be due to precession instead of Earth's orbit around the Galaxy. Precession is Earth's "wobble", the "rotation" of Earth's own axis of rotation. Like how a top wobbles around as it spins. It takes about 26,000 years for the Earth's axis of rotation to make "wobble around" in one cycle. So this is the larger cause of the night sky, and the pole star, looking different for the ancient greeks. But this impacts the apparent position of all stars in the sky. So Ancient Greeks could see certain constellations that are currently too far below the horizon for their contemporaries. The positions of these constellations have changed.
Earth's or the solar system's orbit around the galaxy takes about 230 million years, so this would have less of an impact.
But there would be some differences.
The stars are moving though as they orbit around the Milky way. Some stars move much fast than others and their individual positions could definitely change over thousands of years. From Universe Today
When a star is moving sideways across the sky, astronomers call this “proper motion”. The speed a star moves is typically about 0.1 arc second per year. This is almost imperceptible, but over the course of 2000 years, for example, a typical star would have moved across the sky by about half a degree, or the width of the Moon in the sky.
stars will be farther apart in the sky and eventually as the universe expands, you won't see anything except pitch black.
I once went to a Wikipedia page with a title like "the far timeline of the universe" or something. Putting it poetically - I think it was that the stars go out on earth in ~100b years.
100–150 billion The Universe's expansion causes all galaxies beyond the former Local Group to disappear beyond the cosmic light horizon, removing them from the observable universe.
I guess Windows 1087 won't allow you to reconnect to Local Group unless you have Windows 1087 Pro.
The far future is truly Lovecraftian and hard to fathom. Eventually star formation will cease, most of the timespan of the universe will be the "dark era" where black holes slowly evaporate due to Hawking Radiation. Then there will only be light, and when there is only light then time itself ceases to exist as a meaningful construct. Space, too, perhaps. Then there is an alternative, even longer ending, if it's possible for light itself to decay.
Semi unrelated but I really love futuretimeline.net for stuff like this. In the shorter term they try to make predictions on a human scale but the extreme long term is all astronomical stuff since it's the only thing that can be predicted millions of years in the future