OP states all the other stairs in the house have a tread depth of 10.75" but after the contractor redid the basement stairs they have only 9.5" of tread depth. Pics in comment by OP are consistent with tread depth 9.0" (not 9.5") and rise 7.5". OP should edit the question to put the link to the pics there. (Can leave the link in the comment, and just add link to the question.)
OP reports the basement stairs walk differently after the work, are cramped. OP thinks the contractor left the old risers in place and added new risers by fastening them to the faces of the old risers. The may be the accepted way to add hardwood treads and risers to a stairs which were originally built for carpet. The original 2x lumber is left in place and treated as subflooring for treads and for risers.
The original stairs had a significant overhang of the treads past the original risers which might have been 1" or a little more and would have been exaggerated due to having carpet over nearly sharp 90 deg edges. On the new treads the nosing is more rounded in cross section, is slick hardwood, and may not protrude as far. This would shorten the tread depth.
It is hard to understand how these two factors could account for the tread depth being reduced from an original 10.75" to the current 9.5".
What to do now? I would not accept a modification to stairs that presented a safely hazard that was not present in the original construction.
It could be that in some parts of the US it was common to have basement stairs that were inferior to the stairs in the regular living space, but IMHO this is not acceptable in the present day. In fine homes in the UK and maybe in the US I believe there were servant's stairs that were steeper (higher rise and shorter run) and with shorter treads than the owner's stairs in the house.
If the OP does not have measurements of rise, run and tread depth of the original stairs with carpet removed, then she should ask the contractor if he measured that and has the measurements. In any case, the contractor should have informed the homeowner that the redo as planned would reduce the tread depth and make the stairs harder to use than the original construction. Even if 9.5" is the allowed minimum, it is not as convenient as 10.5" and is significantly different from all the other stairs in the house.
There is a standard that the rise + run = 17" to 18". But it seems that in practice in using this standard the tread depth is used in place of run. This suggests that perhaps the stairs could be made more like the rest of the stairs in the house by extending the nosing to the maximum allowed. But could this be done without removing the treads?