Fix deploy test TypeScript exclusions (#96545)
## Summary
Set `NEXT_PRIVATE_LOCAL_DEV=1` for directory fixtures in deploy mode,
matching the next-start setup. This keeps copied test runner files
excluded from TypeScript checks when deployment tests use
`tsconfig.test.json`.
## Verification
- `pnpm exec tsc --project test/lib/tsconfig.json --noEmit`
- Not run: deployment tests (requires Vercel deployment credentials)
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