Sync nextjs examples to @arkenv/nextjs 0.1.6 (#1844)

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## Description

Restores examples sync after the `@arkenv/nextjs` `0.1.6` version bump
from Version Packages (#1841).

`pnpm sync:examples` updated:
- `examples/with-nextjs` and `examples/with-nextjs-strict`
`package.json` (`@arkenv/nextjs`: `^0.1.5` → `^0.1.6`)
- matching `package-lock.json` files for those examples

This fixes the failing `check-sync` job on the Sync `dev` → `main`
workflow.

Verified: `pnpm sync:examples:check` exits 0.

## Type of Change

- [x] Bug fix (non-breaking change which fixes an issue)

## Checklist

- [x] My code follows the code style of this project (double quotes,
tabs, no parameter reassignment).
- [x] I have written sentence-case imperative commits / PR title (e.g.
`Add support for custom error messages` - no `feat:`, no trailing
period, capitalized).
- [ ] I have added tests to cover my changes.
- [x] All new and existing tests passed.
- [ ] I have created a changeset using `pnpm changeset` (if this affects
a published package).

### For v0 (dev) PRs:
- [ ] **Forward-Porting**: (For maintainers) Has this change been
manually forward-ported to the `v1` branch?

No changeset needed — examples-only sync, no published package source
changes.


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Co-authored-by: Cursor Agent <cursoragent@cursor.com>

Author: yamcodes