In the sentence, "leisurely" modifies the noun "stroll" (a short walk). Any word that modifies a noun or pronoun is an adjective.

১. Although it ends in "-ly", it functions as an adjective here because "stroll" is a noun.
২. It cannot be an adverb because it is not modifying a verb or an adjective in this context.
৩. A noun would represent a person, place, or thing, which "leisurely" does not do.

অতিরিক্ত তথ্য: Other examples of "-ly" adjectives include "friendly", "lovely", and "heavenly".