Put a good sized “beam” at the transition.

Paint the ceilings all one color in flat finish…any color you love, or white…but flat finish.

Replace both the fan and the living room ceiling light with matching ones…choose downlight only, so light isn’t bouncing up on the ceilings, showing differences.

We had exactly same issue; textured dining room ceiling and flat kitchen ceiling. A contractor friend of ours was able to flatten out the textured area by doing a skim coat of plaster of Paris; i believe he did two coats with some light sanding in between and he blended it to the kitchen ceiling. We primed and painted both kitchen and dining area twice and it looks great now. The reason we had it done was because we had water damage to the the textured ceiling.