Inspired by Claude Code's /branch command. Creates a copy of the current
session's conversation history in a new session, allowing the user to
explore a different approach without losing the original.
Works like 'git checkout -b' for conversations:
- /branch — auto-generates a title from the parent session
- /branch my-idea — uses a custom title
- /fork — alias for /branch
Implementation:
- CLI: _handle_branch_command() in cli.py
- Gateway: _handle_branch_command() in gateway/run.py
- CommandDef with 'fork' alias in commands.py
- Uses existing parent_session_id field in session DB
- Uses get_next_title_in_lineage() for auto-numbered branches
- 14 tests covering session creation, history copy, parent links,
title generation, edge cases, and agent sync
