fix(app): populate project picker from home

[Brendonovich]

Summary

• preserve indexed directory results from server versions that support them
• fall back to the current home-directory listing when indexed search returns no results
• locally fuzzy-match typed queries such as documents against that listing
• show every directory returned for an empty fallback query
• keep the compatibility behavior entirely in the frontend directory picker

Testing

• bun test --conditions=solid --preload ./happydom.ts ./src/components/directory-picker-domain.test.ts in packages/app
• bun typecheck in packages/app
• pre-push repository typecheck (30 packages)

Visual verification

• 1440x900 dark-mode comparison: dev shows an empty picker, while this branch shows folders from the home directory