Per the given definition of the use of demeurer, je suis demeurê makes no sense since the question refers to a state of mind and not a location. Why is that given as the correct answer?
Hard to respond without the question, but ‘je suis demeuré ….’ would be correct for a state of mind, a state of being (physically or metaphysically) - synonym for ‘rester’ .
‘Avoir’ is used when demeurer is a synonym for ‘résider/habiter’ (not just ‘stopped’ somewhere.
See the definitions and usage in Larousse: https://www.larousse.fr/dictionnaires/francais/demeurer/23301
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