Dry wall screws used on new stairs

Personally I would use decking screws dry wall tend to snap

Dry wall screws shouldn’t be used for staircase. They should be wood screws and if you can use a good quality not cheap ones as they snap easier

Yes if you were to remove the drywall screws and replace them with good quality wood screws this will definitely add strength, if you were to over tighten a drywall screw it will snap but by using a wood screw you are able to pull everything together nice and tight with out snapping and as a result alleviating the squeaking treads. Also try to add low expansion wood glue to the joists before screwing them together. And add addition supports to the underside of the stairs.

I can say. If the staircase has been built and glued. There should be no reason for squeaking if you leave the the glue to cure for 24 hours. If you walk on it beforehand . It will squeak

The risers should be glued into underside of tread in a groove & Countersunk 4.5mm x 40mm Wood screws should used in all risers connecting to treads, If treads & Risers are MDF construction these should be pre drilled with a 2.5/3mm pilot drill bit to prevent treads splitting Dry wall screws should never be used on stairs as they are to soft & not strong enough & also the stairs will creak Hope this helps