feat: migrate off Nx to Vite+

[chrisjwalk]

Overview

Phase 2 of the migration spike from #147. Replace Nx task orchestration, ESLint, and Prettier with Vite+ tooling.

Phase 1 (Analog.js app build + content) is complete.

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Changes required

• Add package.json to each of the 7 libs (auth, counter, home, login, shared, todo, weather-forecast) so Vite Task can derive ordering from workspace dependencies
• Run vp migrate --no-interactive from workspace root — rewrites Vitest imports to vite-plus/test, merges configs
• Replace nx.json + project.json lint/test targets with run.tasks in vite.config.ts
• Replace custom .NET Nx executors (tools/builders/dotnet-builder) with vp run task definitions calling dotnet CLI directly
• Replace nxViteTsPaths() with vite-tsconfig-paths plugin (same behaviour, no Nx dependency)
• Swap @nx/enforce-module-boundaries ESLint rule for a convention-only approach (TS path aliases already enforce boundaries)
• Replace CI's nx affected with --filter + a git diff-based shell script

Toolchain delta

Removed	Replaced by
All @nx/* packages	vite-plus
ESLint + Prettier	Oxlint + Oxfmt (Rust-based, ~50–100× faster)
nx.json + 9× project.json	single vite.config.ts

Acceptance criteria

• All @nx/* packages removed from package.json
• vp dev, vp build, vp test all pass for all projects
• Lint and format work via Oxlint + Oxfmt
• .NET build/test still works via vp run
• CI updated to use --filter instead of nx affected
• All existing unit and e2e tests pass

References

• Spike: Spike: migrate from Nx to Vite+ via Analog.js #147
• Vite+ docs: https://vite.plus