Drew had a bit of a challenge recovering these carpeted stairs, as the underlying structure was not in very good shape.. I might suggest based on his experiences that you really check out the old stairs, once the carpet has been removed to see what’s happening.
If the old steps have a wear spot ie. dished out in the middle that rarely causes a problem in installation… you just add more and better quality glue (like PL premium) so you’re sure that the new step makes contact and adheres to the underlying structure.
In his case the step was “crowed” as in “bubbled up”. This is a more challenging dilemma. Often found in homes where the wood used at the time of construction was not dry. If you’re lucky and have a power hand planer or grinder you can often remove minor hills. If it is really bad you are best off to remove these old steps and replace them with plywood covers. Then add your new steps to the top of this.