feat: label sessions by runtime

[raphant]

Summary

• Add optional runtime metadata to the mirrored session protocol.
• Mark Claude, Codex, and Pi sessions at each runtime source.
• Show visible CLAUDE, CODEX, and PI badges in the session palette.
• Include available runtime metadata in session search.
• Omit the badge when older or partial session data has no runtime.

Verification

• Root tests: 36 passed.
• Extension tests: 39 passed.
• Extension source and test type checks passed.
• Web, webview, extension, and standalone builds passed.
• git diff --check passed.
• The live dashboard showed both PI and CLAUDE badges in the accessibility tree.
• Searching for pi returned only Pi sessions.

This implements the runtime-identification slice of issue #1.
It does not close the remaining project, worktree, branch, model, and session-total metadata scope.