Update Next.js to 16.2

[charlesrhoward]

Summary

Update Next.js to 16.2 across all apps and examples.

Current versions:

• apps/playground: 16.0.10
• examples/classic-v0: 15.5.9
• examples/v0-sdk-react-example: 15.5.9
• examples/simple-v0: 15.5.9
• examples/v0-clone: 15.5.9

Tasks

• Update next dependency to 16.2 in all package.json files
• Run pnpm install to update lockfile
• Review Next.js 16.2 release notes for breaking changes
• Run build for all apps/examples and fix any issues
• Test critical flows locally

[Mishra-coder]

Hi! I’d like to work on this issue. Could you please assign it to me? I’ll make sure to follow the contribution guidelines. Thanks!