docs: update batteries, deployment, and project documentation

- BATTERIES.md: rewrite to match actual source, add Pagination/Caching/Social OAuth - README.md, CONTRIBUTING.md, CLAUDE.md, DEPLOYMENT.md: various improvements

Author: Adjanour

CLAUDE.md

@@ -41,7 +41,7 @@ Handlers switch on `result.type` and map to HTTP responses.
 
 ## Module Structure
 
-```
+```bash
 modules/{name}/
   routes.ts         # OpenAPI route definitions
   handlers.ts       # HTTP handlers
@@ -86,10 +86,12 @@ import { addJob } from "@/jobs";
 ## Environment
 
 Required in `.env`:
+
 - `DATABASE_URL`
 - `BETTER_AUTH_SECRET` (32+ chars)
 
 Optional:
+
 - `REDIS_URL` — for jobs/caching
 - `S3_*` — for file uploads
 - `RESEND_API_KEY` — for email

CONTRIBUTING.md

@@ -66,7 +66,7 @@ try {
 
 Be specific. Say what changed and why.
 
-```
+```git
 # Good
 fix(auth): handle expired refresh tokens
 

README.md

@@ -165,7 +165,7 @@ See [docs/DEPLOYMENT.md](docs/DEPLOYMENT.md) for the full guide.
 
 ## Project Layout
 
-```
+```bash
 apps/backend/src/
   modules/         ← Your features go here
   lib/             ← Reusable utilities