Move chat toggle to sidebar + needs to be able to be disabled

The new chat was just enabled for me, and right now the chat toggle is super intrusive and covers page content on my secondary monitor:

It would fit better in the sidebar where it’s not covering page content. Right now it just fights with the existing web layout too much. There should also be an official way to disable it permanently, because I don’t want people contacting me through the chat. It’s not because the feature is lacking, but because I would rather have people PM me which I can respond to at my own leisure instead of being always readily available (time sink).