feat(git): Add nested AmazonQ.md files to .gitignore and implement distribution mechanism

## Description
We need to add any nested `AmazonQ.md` files to `.gitignore` and implement a mechanism to distribute the main `AmazonQ.md` file to all nested directories in the repository.

## Background
As part of our development experience with AI coding tools, we're using `AmazonQ.md` files to provide context to Amazon Q. Currently, these files need to be manually maintained across different directories, which is error-prone and time-consuming.

## Proposed Solution
1. Add a pattern to `.gitignore` to exclude nested `AmazonQ.md` files
2. Create a script or git hook that automatically copies the main `AmazonQ.md` file to all nested directories

## Implementation Options
- **Git Hooks**: Create a pre-commit or post-checkout hook that distributes the file
- **Setup Script Integration**: Extend the existing setup.sh to handle this distribution
- **Makefile Target**: Add a target to distribute the files on demand

## Benefits
- Consistent context for Amazon Q across the entire repository
- Single source of truth for Amazon Q context
- Follows our "automation mindset" principle from the dotfiles philosophy
- Supports the "spilled coffee" principle by making the setup reproducible

## Tasks
- [ ] Update `.gitignore` to exclude nested `AmazonQ.md` files
- [ ] Create distribution mechanism (hook or script)
- [ ] Document the approach in the README
- [ ] Test on different environments

## Notes
This is a spike to evaluate the feasibility and approach. The implementation should align with our dotfiles philosophy of automation and reproducibility.

Related to: Development experience, AI coding tools

Start by inspecting the existing .gitignore, setup.sh, and README to understand current setup and documentation conventions. Compare the proposed hook, setup-script, and Makefile approaches, then test the chosen mechanism across the environments named in the issue. Done means nested AmazonQ.md files are ignored, distribution is reproducible, and the approach is documented.

Written by the indexing model from the issue text.