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>

nix/mkViteApp.nix

@@ -12,8 +12,7 @@ pkgs.buildNpmPackage {
   makeCacheWritable = true;
 
   nativeBuildInputs = with pkgs; [
-    nodejs
-    nodePackages.npm
+    nodejs_22
     util-linux  # For script command to create pseudo-terminal
   ];