fix: cannot build/run locally due to missing workspace dependencies

[omsherikar]

Bug Report: Missing Workspace Dependencies & Build Configuration Issues

Describe the bug
The current repository cannot be built or run locally in a strict environment (e.g., fresh clone) due to missing dependencies in workspace packages (packages/ui, packages/lib) and inconsistent TypeScript path aliases. The build fails with multiple Module not found errors.

To Reproduce

1. Clone the repository
2. Run bun install
3. Run bun run dev (or cd apps/web && bun run dev)
4. See error: Module not found: Can't resolve 'motion' (and others)

Current Behavior

• The build or dev server starts but crashes immediately or fails to compile specific components.
• Terminal output shows multiple Module not found errors pointing to packages/ui or packages/lib.
• CSS compilation fails with @import "tailwindcss" errors.
• The web application returns 404s or 500s when accessed.

Expected behavior
The application should build and run successfully after installing dependencies, as described in CONTRIBUTING.md.

[linear]

ENG-560