chore: Update with-changesets example (#14638)
## Summary
Modernize only `examples/with-changesets`:
- Pin direct dependencies to current registry releases, including
Next.js 16.4.0, React 19.3.0, TypeScript 7.0.2, ESLint 10.12.0,
Changesets 3.0.3, and Turbo 2.11.7; use pnpm 12.11.2 and Node.js
26.11.1, and regenerate the pnpm lockfile.
- Replace legacy ESLint configuration and `next lint` with flat
configurations. Parse TypeScript with Babel independently of the
compiler API, and use explicit compiler checks for types and unused
declarations.
- Migrate library bundling to tsdown 0.23.1 with ESM/CommonJS
conditional exports, matching declarations, React peer dependencies, and
preserved client directives.
- Refresh TypeScript settings, remove the unused Node 14 preset and
nonexistent test task, and add dependency-aware type-checking tasks with
Next.js route type generation.
- Correct README commands to pnpm and update the Changesets schema and
release workflow to current action versions, explicit permissions,
frozen installs, and the configured versioning script. Remove the
non-runnable placeholder Slack command.
## Manual verification
Loaded both libraries through ESM imports and CommonJS requires,
verified matching exports, client directives, and declaration files,
rendered the Button with React's server renderer, and checked the slug
utility through both module formats. No packages were published.
Co-authored-by: vercel-gh-bot-3[bot] <282332853+vercel-gh-bot-3[bot]@users.noreply.github.com>