Generate TypeScript types from the OpenAPI spec

[Jayy4rl]

Context: Issue 127 adds an OpenAPI 3.1 spec. Frontend developers need TypeScript types auto-generated from it so they stay in sync with the API.

Requirements:

• Install openapi-typescript as a dev dependency.
• Add "generate-types": "openapi-typescript api/openapi.json -o src/generated/api-types.ts" to backend/package.json.
• Commit the initial generated file.

Acceptance criteria:

• npm run generate-types produces a valid TypeScript file with no type errors.
• Types match all request/response schemas in the OpenAPI spec.