Idea: Add (optional) local timezone to client-originating events

Nobody has claimed this yet.

**Is your feature request related to a problem? Please describe.**
I was talking with a friend on/off and they kept getting confused by our timezone difference (about 8 hours).

**Describe the solution you'd like**
It would be a neat quality of life improvement to allow clients to send an optional timezone or full timestamp with timezone information to allow clients to display the timezone that the person you are talking with is in.

**Describe alternatives you've considered**
n/a

**Additional context**
Matrix already federates messages with `origin_server_ts`, keeping it backward compatible would likely mean introducing another parameter - be it just the timezone or a full timestamp with timezone information.
Alternatively this could be stored in the room state.
Alternatively alternatively clients can roll their own feature to show manually set-up timezone differences and no change to the protocol would be required.

Start by reviewing the Matrix protocol's existing origin_server_ts handling for client-originating events. Compare the proposed optional timezone, full timestamp, and room-state alternatives, then define a backward-compatible protocol change and document its behavior.

Written by the indexing model from the issue text.