Provides initial implementation of new chat overlay in component
`ChatOverlayV2`. Contains only the basic functionality required for
a functioning chat overlay according to the new design with the intent
of added the rest of the functionality in subsequent PRs.
Backports existing tests for the current chat overlay except for ones
testing keyboard shortcuts (since they haven't been added) and tab
closing behaviour (since no tabs).
This was in flyte's design (he was following discord) but doesn't feel
too correct when it's not aligned with anything else. We can revisit
this if/when we have better glyphs to represent channel types.
