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>

.gitignore

@@ -66,3 +66,7 @@ out
 .github/instructions/nx.instructions.md
 
 .env.local
+
+# Nix
+.direnv
+result