If you lay a finish on top of a stair with any thickness and you don't similarly cover the landing and floor above and the hall below, the added thickness will affect the rise of the first and last steps and may cause a trip hazard going in either direction.
ONQ.
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All advice on AAM is remote from the situation and cannot be relied upon as a defence or support - in and of itself - should legal action be taken.
Competent legal and building professionals should be asked to advise in Real Life with rights to inspect and issue reports on the matter at hand.