chore: migrate to Nix flakes, remove Docker and legacy configs

Remove all Docker files, Vercel config, Verdaccio, and old CI workflow.
Standardize on nodejs_22 across devShell and nix build helpers.
Update CI to build all packages and push to Cachix on merge to develop.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

package.json

@@ -133,7 +133,6 @@
     "tw-animate-css": "^1.2.8",
     "typescript": "5.9.3",
     "typescript-eslint": "8.40.0",
-    "verdaccio": "^6.0.5",
     "vite": "7.1.3",
     "vite-plugin-dts": "~4.5.0",
     "vitest": "^3.0.8"