Question

If our orbit around the sun slowed down how would that affect the way we observe constellations?

Answer 1

As it takes the sun about 250 million years to orbit the galaxy, the proper motion of stars relative to the Sun will be the dominant effect of changes in the sky. The visible effects of the rotation will be far slower.

All stars move in the sky, some faster some slower, and in more or less random directions, not just moving around the galaxy.