feat(examples): add TypeScript types to next-js example

[evan976]

This PR brings TypeScript to the Next.js example:

• Files converted to .ts/.tsx
• Typed components props

Example still works normally (pnpm dev in examples/next-js).
All checks pass (type-check, lint, build).

No core package changes.

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Greptile Overview

Greptile Summary

This PR updates the Next.js example’s featured-section.tsx to use TypeScript by adding inline prop typings to several example components (e.g., WalletModal, WalletDropdownContent, and Base UI variants). These changes are confined to the example UI layer and don’t touch the core connector packages.

One behavioral change is included: the Base UI menu popup className drops the outline utility while keeping outline-1 outline-gray-200, which likely removes the intended outline styling.

Confidence Score: 4/5

• This PR is safe to merge once the Base UI popup outline class regression is fixed.
• Changes are limited to example TypeScript prop typing, with one concrete UI regression: removing the outline utility prevents outline-1/outline-gray-200 from taking effect, changing the rendered styling.
• examples/next-js/components/playground/featured-section.tsx

Important Files Changed

Filename	Overview
examples/next-js/components/playground/featured-section.tsx	Adds inline TypeScript prop types to several exported components; one className change removes the outline utility, which likely breaks the intended outline styling on Base UI menu popup.

Sequence Diagram

sequenceDiagram
    participant User
    participant ConnectButtonBaseUI
    participant Menu as BaseUI Menu
    participant WalletDropdownContentBaseUI

    User->>ConnectButtonBaseUI: Click trigger button
    ConnectButtonBaseUI->>Menu: Open popup
    Menu->>WalletDropdownContentBaseUI: Render dropdown content
    Note over Menu: Popup className lost `outline` utility
    Note over Menu: outline-1/outline-gray-200 won't apply
    User-->>Menu: Sees missing outline styling

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Project	Deployment	Actions	Updated (UTC)
connectorkit-playground	Ready	Preview, Comment	Feb 13, 2026 7:43am