For competitions in completely airgapped environments with no internet
access, all dependencies must be vendored before deployment. This commit
adds complete documentation and automation for airgapped deployments.

Changes:
- Add docs/source/installation/airgapped.rst: Comprehensive guide for
  airgapped deployments including preparation, deployment, and
  troubleshooting steps
- Add bin/create-airgapped-package.sh: Automated script to build and
  package all Docker images and dependencies for airgapped deployment
- Update claude.md: Add airgapped deployment guidance for AI agents
  working with the codebase
- Update README.md: Reference airgapped deployment options
- Update docs/source/installation.rst: Include airgapped documentation
  in table of contents
- Update docs/source/installation/docker.rst: Add note pointing to
  airgapped guide

The new script and documentation cover:
- Docker image vendoring (Python, Redis, MariaDB, Nginx, all app images)
- System package vendoring (apt packages)
- Python dependency vendoring (pip packages)
- Complete deployment workflow for offline environments
- Backup, restore, and troubleshooting procedures

This ensures competitions can run successfully in completely isolated
environments without any external network dependencies.