Builder agent picker and safer agent edits

What changed

• Builder projects can now run on the AlgoArena agent, Claude Code, Codex, or both terminal agents. The terminal agents start in the background, so their tab is ready when you open it.
• The Builder start screen now has the same mode, permission, and model pickers as the workspace, and your choices carry into the project's first chat.
• Agent edits now show in the preview as soon as they land. A rewrite that would wipe out most of a file is refused, and the agent is told why.