Add GitHub chat panel

[yZangEren]

Addresses inquid/github-chat#1.

Summary:

• Adds a GitHub-wide Chat toggle as a separate content script and stylesheet.
• Stores messages per repository or GitHub page with chrome.storage.local and a localStorage fallback.
• Handles GitHub soft navigation so the panel updates context without requiring a full reload.
• Adds clear-history, keyboard submit, message count, and README documentation.

Validation:

• node --check github-chat.js
• node --check content-script.js
• Parsed manifest.json with JSON.parse
• git diff --check
• Playwright + Edge unpacked-extension verification:
  • loaded the local extension
  • opened https://github.com/inquid/github-stories
  • sent a chat message and verified it persisted after reload
  • opened https://github.com/explore and verified the system-page chat context