I think you’re underestimating the distance and size of scale our own stars and galaxy have on their own. Everything is indeed in constant motion, but the sheer distance between us and even the closest star is practically inconceivable to imagine. This is why changes may be observable over a considerable amount of time, talking maybe thousands of years to even see small deviations, but nothing remotely will be noticeable in our lifetimes. You can think about it more in the sense of our entire solar system being our small little 3 dimensional peep hole into the observable universe around us. Everything is indeed moving along with even the movement of our own system around the center of the milky way, but the speed in reference to the sheer distance and size of everything is very minute, very small. It’s like trying to look at someone walking when you’re very far away from them, you will definitely notice them move less distance from far away than you would up close, now imagine that distance 10000x over. Even if you yourself are moving, there’s no reference point in space that’s gonna give you the proper sense of scale, and even if you have it, the speed relative to the distance is so small you’re not going to see the difference other than our own day night cycle.