On the small-screen layout, the popover goes down and covers the item
list, which isn't a big deal in context; so I want it to be basically
as tall as it can be without being unwieldy, to give more info.
But on the large-screen layout, it doesn't take long at all for the
popover to start intersecting the pet preview, because it *has* to go
up and cover the pet preview. So, I'm much more reserved about how much
vertical space I'm willing to give it!
(I also considered sending the popover off to the *right* of the button,
to cover the item list, but it felt *way* too weird imo! Especially in
the expressions case.)