Website sprint: refresh Project_Index to include all public repos + categorize

[flightgod]

Update the public Project_Index repo so it lists all public repos and stays current.
Decide whether it should index only client-facing BadgePiratesLLC repos or also include a future BadgePiratesResources org.

Acceptance:

• Repo list updated
• Basic categories (docs/blog/firmware/badges/tools)
• Document update procedure (manual or script)