refactor: finalize standalone services cleanup

- Remove root pnpm-lock.yaml (stale monorepo lockfile)
- Rename root package from bete-monorepo to bete
- Clean up root scripts to use cd instead of pnpm --prefix
- Remove ignoreScripts/trustedDependencies from frontend package.json
- Optimize Dockerfiles with multi-stage builds and proper layer caching
- Update .dockerignore to exclude build artifacts
- Remove leftover pnpm test config file from frontend

.dockerignore

@@ -1,11 +1,21 @@
 node_modules
 dist
+.next
+out
 .env
-.env.test
+.env.*
 .git
-.github
-recordings
+.gitignore
+.claude/
+.vscode/
+.design/
+design/
+docs/
+scripts/
+test_out.nut
 *.db
 *.db-shm
 *.db-wal
-test_out.nut
+*.log
+*.md
+.DS_Store