Previously hidden sidebar state is not restored when exiting search mode
As soon as you enter search mode, Papers shows the sidebar if it was not already shown (for search results). However, unlike Evince (and what you would expect), Papers leaves the sidebar open after use when you dismiss the search (whether with the Esc
key or clicking the search toolbar togglebutton again) and reverts it to the thumbnails list, even if you didn't want the sidebar/thumbnails shown in the first place.
Comparing the two apps (Evince on the left, Papers on the right):