fix(sessions): restore provider and working directory from live panes

[Lint111]

Summary

• persist each session provider as a tmux user option when a pane is created or respawned
• recover provider and working-directory metadata from live panes during reconciliation
• migrate legacy panes by inferring their provider once from the live process command
• preserve explicit remote and Docker workspace metadata

Root cause

When mux-sessions.json was missing or contained an older recovered placeholder, reconciliation rebuilt an untracked pane with mode: "claude" and workingDir: process.cwd(). The tmux pane itself survived, but Codeman lost the provider and repository context needed to restore the session accurately.

The provider is now durable in @codeman-mode, while #{pane_current_path} supplies the live local working directory. Existing panes without the option are inferred from their process command and migrated back into tmux metadata. Stale restored-* paths are repaired even when Codeman restarts from a different server directory.

Safety and compatibility

• provider values are constrained to the existing SessionMode allowlist
• discovered mux names and pane paths continue through existing validation
• process IDs are parsed as numbers before the ps fallback
• remote and Docker sessions never replace their modeled workspace with a local pane path
• legacy pid-only and path-bearing list output remains parseable

Commit structure

1. fix(sessions): restore provider and working directory from live panes

Validation

• npm test -- --run test/tmux-manager.test.ts (59 tests)
• npm run typecheck
• npm run lint
• npm run build
• npx prettier --check src/tmux-manager.ts test/tmux-manager.test.ts
• git diff --check

Scope

This PR does not include working-directory mutation UI, repository-viewer changes, terminal history streaming, or browser terminal lifecycle caching.