feat: add support for updated custom runtime base image tags and documentation examples

## Description
As the AWS Lambda ecosystem evolves, developers frequently look for updated base image options, optimized runtime layer configurations, and clearer documentation examples for custom architectures.

This issue proposes adding enhanced configuration examples and verification steps for custom runtimes within the repository's documentation guides to streamline deployment workflows.

## Proposed Changes / Features
- [ ] Update documentation examples for modern container workflows.
- [ ] Provide clear instructions for verifying base image tag compatibility.
- [ ] Add troubleshooting notes for common build-time edge cases.

## Environment & Context
- **Repository:** aws/aws-lambda-base-images
- **Component:** Dockerfiles / Documentation Guides

Start with the repository's Dockerfiles and documentation guides, then review the existing custom runtime examples and base image references. Update the examples, add instructions for verifying tag compatibility, and document common build-time edge cases; the work is done when all three proposed documentation changes are covered.

Written by the indexing model from the issue text.