I don't have any special domain knowledge in this space, but I know that's an advertised use case for emotional support animals.[0]
I don't know if the client needs the service animal around 24/7, but if you have severe PTSD and could experience severe symptoms unexpectedly while shopping, it seems reasonable to bring along the support animal.
That's kind of what I mean: reading that page, it just sounds like normal pet ownership, with many of the benefits that many pet owners get. That's a great thing to encourage and research, but it's not clear to me why there needs to be a special "emotional support animal" classification or the like.
I don't know if the client needs the service animal around 24/7, but if you have severe PTSD and could experience severe symptoms unexpectedly while shopping, it seems reasonable to bring along the support animal.
[0] https://www.nih.gov/news-events/news-releases/service-dogs-m...