Maintenance: retire the repository sample application

[dreamorosi]

Summary

Retire the full sample application under examples/app. This follows the maintainers' decision surfaced during #5618, where sample-application contribution guidance was removed ahead of the app's retirement.

The application remains a root workspace, a root Vitest project, and the target of dedicated jobs in both the PR workflow and merge-queue workflow. The public documentation also still describes the examples directory as containing a full deployable application in the README and docs/index.md.

Why is this needed?

The sample app adds dependencies, tests, CI jobs, and documentation that maintainers must keep current despite the decision to retire it. Removing it completes the related documentation/process cleanup and leaves examples/snippets as the maintained in-repository example source.

Which area does this relate to?

Automation, Tests, Other

Solution

• Delete examples/app.
• Remove examples/app from root workspaces and regenerate package-lock.json.
• Remove the check-examples job from reusable-run-linting-check-and-unit-tests.yml, including its entry in the unit-tests-complete dependencies.
• Remove the check-examples job from quality_check.yml.
• Remove examples/app/vitest.config.ts from the root Vitest projects.
• Remove the app-specific Markdown lint exclusion from package.json.
• Update CODING_STANDARDS.md, the README, docs/index.md, and any remaining repository references that specifically describe or link to the full sample application.

Acknowledgment

• This request meets Powertools for AWS Lambda (TypeScript) Tenets
• Should this be considered in other Powertools for AWS Lambda languages? i.e. Python, Java, and .NET

Future readers

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