The request makes sense to me too, especially as a user-led decision.
For fullscreen chat, it’d be neat if this could be something users could easily control in chat itself, rather than a user setting. Slack, for example, let’s you drag-and-drop the entire Channels (or DMs) area to rearrange the sidebar.
I don’t know how well that would translate to drawer or mobile, though, so maybe the setting is best. Happy to follow your lead @chapoi on what interaction you think makes most sense.