refactor: extract templates from public/

- Created /templates for main site (header.php, footer.php)
- Created /templates/admin for admin section (head.php, footer.php)
- Removed /public/includes and /public/admin/inc
- Updated all references in code and docs
- Tests passing ✅

Cleaner separation: /public only contains web-accessible files (PHP entry points + assets)

src/cache/rate_limit/ad921d60486366258809553a3db49a4a.json

@@ -1 +1 @@
-[1770894771]
+[1770894924]