No problem 
As far as I recall logging out of the app has always made you go through the email “magic link” process. If you’ve now got fingerprint authentication turned on you’re safe to just close the app.
RE live chat.
Monzo were getting inundated with too many questions that people could find the answer to themselves quite easily. So a lot of the wait time was down to people asking things that could be answered in one sentence.
Monzo now want you to search the help articles to “self help” first before contacting them. If you don’t find anything in there I believe you’ll then see an option to open a chat.
Edit:
It’s worded much better from someone at Monzo here: