Load standard project context in rooms

CLI sessions automatically load project context files such as AGENTS.md, but persistent web rooms do not. Rooms should discover and use these files from their configured workspace so the same project instructions apply across Exxperts surfaces and other agent harnesses.

Trace how CLI sessions locate and load AGENTS.md and how persistent web rooms initialize their configured workspace. Confirm which standard context files are discovered and define completion as rooms applying the same project instructions as CLI sessions across the configured workspace.

Written by the indexing model from the issue text.