feat(ui): add start project modal

[yicheng47]

Summary

• replace the sidebar directory-picker shortcut with a Start Project modal
• prefill from the default working directory and keep the name derived until manually edited
• preserve project selection and refresh behavior after creation
• move project-scoped start-modal coverage and add focused StartProjectModal tests

Validation

• pnpm exec tsc --noEmit
• pnpm run lint
• pnpm test (40 files, 295 tests)
• manual smoke test

Closes #383