The soil that was backfilled after the basement wall project was NOT packed, watered, and packed again.
sounds like they just threw some dirt on the area and smoothed it out and never did the packing process. Dirt will melt down to about 1/2 its height when properly watered and tamped.
I would back fill the side walk with pure sand. Add about one foot, then water, then again.
Then when you are almost packed to the height of the side walk under side, add a 25 pound bag of Bentonite. this stuff is used to do just what you need it to do. It expands and exerts upward pressures on the slab from the ground up. Pretty cheap stuff. You can find this at any foundation service company.
I think that you are OK except for the shoddy backfilling job.