feat(logout): add dot logout command

[UtkarshBhardwaj007]

Summary

• Adds dot logout — signs the user out of the host account paired via dot init without having to rm -rf ~/.polkadot-apps.
• Uses the terminal SDK's adapter.sessions.disconnect(session) so the paired mobile app drops its side of the connection too, not just the local CLI.
• Falls back to a best-effort local cleanup — scoped strictly to files prefixed with dot-cli_ in ~/.polkadot-apps/ — when the statement store is unreachable. Narrower than rm -rf; never touches files owned by other polkadot apps on the same machine.

Structure

Mirrors the repo's existing SDK/TUI split so the feature drops in cleanly and is trivial to remove later:

• SDK (src/utils/auth.ts): three new exports alongside connect()/waitForLogin()/getSessionSigner() — findSession(), waitForLogout(), plus an @internal clearLocalAppStorage() used by the fallback.
• TUI (src/commands/logout/): mirrors src/commands/init/'s shape — index.ts (Commander wiring) + LogoutScreen.tsx (orchestrator) + LogoutStatus.tsx (presentational row) + status.ts (pure Ink-free status→row mapping) + status.test.ts.

Notes

• Adapter lifecycle: waitForLogout() owns adapter.destroy() and wraps the whole body in a try/finally, so every control-flow path (including a throwing onStatus callback) releases the WebSocket. Matches the CLAUDE.md invariant that long-lived terminal adapters must always be destroyed.
• No new flags, no confirmation prompt, no alias. logout matches the convention used by gh, docker, firebase, vercel, heroku.
• Dev-mode session keys in ~/.polkadot/accounts.json are deliberately untouched — out of scope for "host account" logout.

Test plan

• pnpm test — 347 tests pass (6 new cases in auth.test.ts covering happy path, err-result fallback, thrown-error fallback, non-Error throws, missing dir, and dot-cli_ prefix scoping + foreign-file preservation; 8 cases in status.test.ts covering every LogoutStatus variant and isTerminal)
• pnpm exec tsc --noEmit — clean
• pnpm run format:check — clean
• pnpm run build — bun build --compile succeeds
• ./dist/dot --help — logout surfaces in the command list
• ./dist/dot logout --help — description renders
• Manual: run dot logout against a real paired session on Paseo, confirm the mobile app drops the connection
• Manual: run dot logout with the People chain unreachable, confirm partial status fires and local files are cleared
• Manual: run dot logout with no session signed in, confirm No account is signed in. and exit 0

[github-actions]

Dev build ready — try this branch:

curl -fsSL https://raw.githubusercontent.com/paritytech/playground-cli/main/install.sh | VERSION=dev/feat/dot-logout bash