chore: Organize repository structure

- Move screenshots from root to docs/screenshots/
- Remove build artifacts (eslint-report.json, tsconfig.tsbuildinfo, out/)
- Remove temporary test files from root (test-sse.mjs, test-watcher.ts)
- Remove tmp/ directory
- Update .gitignore with comprehensive patterns:
  - Build artifacts (eslint-report.json, tsconfig.tsbuildinfo, out/)
  - Temporary files (tmp/, test-*.mjs, test-*.ts, *.tmp, *.temp)
  - Root image files (should be in docs/screenshots/)
  - AI tool directories (.augment/, .claude/, .cline/, .openhands/, .qodo/, .gemini/, .kilocode/)
- Update README image references to new locations

This cleanup makes the repository structure more professional and organized.

.gitignore

@@ -22,3 +22,31 @@ artifacts/
 
 # Archived stashes for reference
 docs/references/stashes/
+
+# Build artifacts
+eslint-report.json
+tsconfig.tsbuildinfo
+out/
+
+# Temporary files
+tmp/
+test-*.mjs
+test-*.ts
+*.tmp
+*.temp
+
+# Root image files (screenshots belong in docs/)
+/image-*.png
+/image.png
+
+# Runtime artifacts
+.beads/
+.agents/
+.agent/
+.augment/
+.claude/
+.cline/
+.openhands/
+.qodo/
+.gemini/
+.kilocode/