Team Directory

Build a team directory page in React with TypeScript. The page fetches team members from /api/team and displays them in a searchable list. Each member card shows their name, role, department, and profile photo.

Users can search by name using a text input that filters the displayed results client-side. There is also an "Invite Member" button that opens a modal form with fields for name, email, and role, which submits via POST to /api/team/invite.

Output

Produce TypeScript/TSX files in a src/ directory:

• src/api.ts -- API client for making requests
• src/types.ts -- TypeScript type definitions
• src/components/TeamDirectory.tsx -- the main directory page with search
• src/components/MemberCard.tsx -- individual team member card
• src/components/InviteModal.tsx -- modal form for inviting a new member
• src/App.tsx -- app root

Do not include test files or build configuration.