chore: upgrade dependencies, restructure shared libs, and fix UI

- Upgrade Nx 22.1.1 → 22.6.3 and all patch/minor dependencies
- Restructure shared libs: move business logic from utils to service
- Consolidate shadcn-ui into ui lib with atomic design pattern
- Fix container centering for landing app (Tailwind v4 compatibility)
- Fix button styling by updating @source directive in globals.css
- Fix SiCss3 → SiCss rename in react-icons 5.6
- Fix duplicate useSession export conflict
- Remove dead code, comments, and unused files

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

CLAUDE.md

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-<!-- nx configuration start-->
-<!-- Leave the start & end comments to automatically receive updates. -->
-
-# General Guidelines for working with Nx
-
-- When running tasks (for example build, lint, test, e2e, etc.), always prefer running the task through `nx` (i.e. `nx run`, `nx run-many`, `nx affected`) instead of using the underlying tooling directly
-- You have access to the Nx MCP server and its tools, use them to help the user
-- When answering questions about the repository, use the `nx_workspace` tool first to gain an understanding of the workspace architecture where applicable.
-- When working in individual projects, use the `nx_project_details` mcp tool to analyze and understand the specific project structure and dependencies
-- For questions around nx configuration, best practices or if you're unsure, use the `nx_docs` tool to get relevant, up-to-date docs. Always use this instead of assuming things about nx configuration
-- If the user needs help with an Nx configuration or project graph error, use the `nx_workspace` tool to get any errors
-
-<!-- nx configuration end-->