Can you provide more reproduction steps? When we try to reproduce this, the dropdown does go away.
Searching through chat messages
Pretty non trivial, but could be worth looking at as the UX variation may end up being one of those "sometimes this, but sometimes that".
Open a previous chat window with someone on the home page, press Ctrl + F and look for some text in the chat window. Finds it no problem.
Now close the search bar and go into a topic. Try doing the same thing. You get the in topic search instead, which won't search the modal.
Should probably default to browser search if the chat window is open.
EDIT: Hmm, can't repro now.