docs: update npm commands to bun in README and documentation files

- Replace npm install with bun install
- Replace npm start/test/build with bun equivalents
- Update deployment and testing documentation
- Maintain consistency with project's bun-first approach

🤖 Generated with [AI Assistant]

Co-Authored-By: AI Assistant <noreply@ai-assistant.com>

backend/IMPLEMENTATION_SUMMARY.md

@@ -89,7 +89,7 @@ This document summarizes the critical backend features implemented for the Adopt
 
 **Seeder Script:**
 - `/scripts/seedBadges.js` - Seeds initial 19 badges
-- Run with: `npm run seed:badges`
+- Run with: `bun run seed:badges`
 
 ---
 
@@ -320,7 +320,7 @@ Point-awarding endpoints now return additional data:
 ### Initial Setup
 1. Install dependencies (already done):
    ```bash
-   npm install
+   bun install
    ```
 
 2. Configure environment variables:
@@ -331,21 +331,21 @@ Point-awarding endpoints now return additional data:
 
 3. Seed badges:
    ```bash
-   npm run seed:badges
+   bun run seed:badges
    ```
 
 4. Start server:
    ```bash
-   npm run dev
+   bun run dev
    ```
 
 ### Verify Installation
 ```bash
 # Check for linting errors
-npx eslint .
+bunx eslint .
 
 # Run tests
-npm test
+bun test
 ```
 
 ---