Show richer session metadata in the session command palette

[raphant]

Problem

The session protocol exposes only an ID, label, state, start time, and last activity time.
The command palette cannot distinguish similar sessions by project, worktree, branch, runtime, model, or cost.

Proposed change

Extend SessionInfo with metadata that each runtime can establish without guessing.
Show available metadata in the command palette and omit fields that a runtime cannot supply.

Acceptance criteria

• The protocol can carry the project path, worktree, branch, runtime, model, and session totals as optional fields.
• Claude, Codex, and Pi populate each field that their event streams establish.
• The command palette searches and displays the available metadata.
• Missing metadata does not produce placeholder or invented values.
• Protocol and palette tests cover partial metadata.

Source

• web/lib/bridge-types.ts defines the web session shape.
• extension/src/protocol.ts defines the canonical session shape.

[raphant]

Runtime identification slice

Pull request #16 implements runtime demarcation at commit 6eb5e47.

The session protocol now carries optional claude, codex, or pi runtime metadata.
Each runtime supplies its verified value.
The command palette shows visible CLAUDE, CODEX, and PI badges.
Session search also matches available runtime metadata.
Sessions without runtime metadata show no invented badge.

The live source dashboard showed PI and CLAUDE rows together in the accessibility tree.
Searching for pi removed the Claude row and retained the Pi rows.

All root and extension tests passed.
All extension type checks and production builds passed.

Still outstanding

This slice does not close issue #1.
Project, worktree, branch, model, and session-total metadata remain outstanding.