[codex] Align README mountApp examples with app registration

[samlaycock]

Summary

Closes #192.

Updates the README Quick Start mountApp(...) examples so wrapper components, custom not-found UI, and navigation behavior options continue passing the explicitly registered app through the options object.

The docs site quick-start examples already used mountApp(root, { app, component: ... }), so the implementation change is limited to the README. I also added regression coverage to the existing docs package-name test to check the README examples alongside the docs-site examples.

Root Cause

The README introduced explicit app registration with mountApp(root, { app }), but the follow-up examples omitted app when adding component, notFound, scrollRestoration, and focusManagement options. That made registered-app setup look optional in examples that build on the same app entry.

Validation

• bun test tests/docs-package-names.test.ts
• bun fmt
• bun lint:fix
• bun test
• bun typecheck
• bun lint

Changeset

Added .changeset/registered-app-readme-examples.md as a patch changeset for the documentation update.

[greptile-apps]

Greptile Summary

This PR fixes four README mountApp code examples that omitted the registered app from the options object, making it look as though explicit app registration was optional in examples that build on it.

• Each affected snippet now includes import { app } from "./app" and passes app as the first option, matching the pattern already used on the docs site.
• Regression assertions were added to tests/docs-package-names.test.ts covering all five README mountApp patterns, using the existing readDoc/normalizeWhitespace helpers.
• A patch changeset is included.

Confidence Score: 5/5

Documentation-only change with no runtime code modified; all four updated examples are consistent with the existing docs-site patterns.

All changes are confined to README prose and a test file. The README examples now consistently pass app through the options object, and the new test assertions correctly exercise each updated pattern via normalizeWhitespace. No logic, API, or package surface has changed.

No files require special attention.

Important Files Changed

Filename	Overview
README.md	Four mountApp examples updated to include the registered app in the options object, with matching import { app } from "./app" statements added to each snippet.
tests/docs-package-names.test.ts	Regression assertions added for all five README mountApp patterns; reads README via the existing readDoc/normalizeWhitespace helpers that collapse whitespace, so multi-line blocks match correctly.
.changeset/registered-app-readme-examples.md	Patch changeset added for the documentation fix; correctly targets the litzjs package.

_{Reviews (1): Last reviewed commit: "docs: align readme mountApp examples" | Re-trigger Greptile}