I am looking at a list of verbs that take essere in the present perfect, and stare is one of them.
others: andare, apparire, arrivare, cadere, diventare, entrare, essere, morire, nascere, partire, restare, rimanere, ritornare, salire, scendere, tornare, uscire, venire, vivere.
It says, "The present perfect of intransitive verbs- those that do not take a direct objecdt- is formed by combining the present tense of essere and the past participle of the verb. Most of these verbs usually express movement (arrivare), lack of movement (stare), a mental or physical state (arrossire), or some process of change (invecchiare)...
Past participles conjugated with essere agree in gender and number with the subject of the verb."
(Practice Makes Perfect: Italian Verb Tenses, p. 80)