fix: make npm typecheck run project checks

[RutamBhagat]

Summary

• fix npm run typecheck to use the project tsconfig instead of printing TypeScript CLI help
• add a root tsconfig.json for type-checking src/**/*.ts and src/**/*.tsx
• keep path alias support (@/*) and no-emit behavior for CI/local checks

Why

Running npm run typecheck currently prints tsc help text instead of checking the codebase.

Closes #207

Stacked PR Context

This is a stacked PR base for the typecheck series. Follow-up stacked branches are:

• fix/typecheck-1
• fix/typecheck-2
• fix/typecheck-3
• fix/typecheck-4
• fix/typecheck-5
• fix/typecheck-6

Output

npm run typecheck

Found 42 errors in 15 files.

Errors  Files
     1  src/components/AuthenticationStep.tsx:14
     1  src/components/ControlPanel.tsx:117
     1  src/components/EmailVerificationStep.tsx:5
     1  src/components/LocalWhisperPicker.tsx:168
     3  src/components/SettingsPage.tsx:1447
     4  src/components/TitleBar.tsx:41
     5  src/components/TranscriptionModelPicker.tsx:47
     1  src/components/ui/MarkdownRenderer.tsx:12
     4  src/components/ui/SupportDropdown.tsx:20
     1  src/helpers/llamaCppInstaller.ts:8
     1  src/hooks/useLocalModels.ts:49
     4  src/hooks/useModelDownload.ts:123
     4  src/lib/neonAuth.ts:6
     2  src/services/ReasoningService.ts:17
     9  src/utils/providerIcons.ts:2