feat: distribute via Homebrew and Winget package managers

[athopen]

Motivation

Users on macOS and Windows expect to install CLI tools through their platform's native package manager. Claude Code sets this precedent — it ships via Homebrew and Winget alongside direct downloads. We should do the same for database-mcp.

Proposal

Homebrew (macOS / Linux)

Create a Homebrew tap so users can install with:

brew install haymon-ai/tap/database-mcp

And upgrade with:

brew upgrade database-mcp

Implementation:

• Create a homebrew-tap repository at haymon-ai/homebrew-tap
• Add a formula that downloads the prebuilt binary from GitHub Releases
• Automate formula updates on release (e.g. via homebrew-releaser or a step in release.yml that bumps the formula SHA and version)

Winget (Windows)

Publish to the winget-pkgs community repository so users can install with:

winget install haymon-ai.database-mcp

And upgrade with:

winget upgrade haymon-ai.database-mcp

Implementation:

• Create a Winget manifest and submit a PR to microsoft/winget-pkgs
• Automate manifest updates on release (e.g. via winget-releaser action in release.yml)

Dependencies

• feat: add macOS and Windows release builds #96 — macOS and Windows release builds must be available first

Documentation updates

• Update docs/content/docs/installation.mdx to add Homebrew and Winget as installation methods
• Update README.md with the new install commands
• Add Homebrew/Winget to the installation comparison table