After changing filter, water dispenser is slow starting and run a few secs after shutting off. Dribbles for about 15 secs. 10 year old G E side by side water in the door

If all you did was change the filter I would suspect either you missed removing something before install (some kind of plug to keep it clean) or you put it in backwards. Some filters have a directional arrow on them to show water flow. Before putting on a new filter it's a good idea to flush the line into a bucket or something to get any sediment out of the line leading to the filter.

What is proper water flow inlet for the GE side-by-side 26cuft fridge