Show user activity and readiness status in rooms

[coder13]

Rooms should show whether users are active, idle, competing, spectating, waiting, or currently solving.

Feedback source:

• User position for what they're doing.
• Show if people are active.
• In users online, you should be able to challenge someone, or invite them to a room.

Acceptance ideas:

• Display per-user room state in the room UI.
• Distinguish at least active/idle/spectating/competing/waiting/skipping if available.
• Use status information to support better leader transfer and host controls.