[web] Persist InputState outside of Chat tab

Summary: This diff moves ChatInputStateContainer outside of Chat. Right now, Chat gets dismounted when the Calendar tab is opened, which leads to the last of input state (such as message drafts).

Test Plan: Make sure drafts are persisted after navigating to Calendar tab and then back to Chat tab

Reviewers: KatPo, palys-swm

Reviewed By: KatPo, palys-swm

Subscribers: zrebcu411, Adrian

Differential Revision: https://phabricator.ashoat.com/D464