feat(frontend): auto-generate TypeScript types from backend OpenAPI schema

Replace manually maintained types in src/lib/types.ts with auto-generated
types from FastAPI's OpenAPI schema using @hey-api/openapi-ts. The bridge
file re-exports generated types with renames, Require<> augmentations for
fields that are optional in the schema but always present in responses, and
manually added relationship fields excluded from OpenAPI.

- Add openapi-ts.config.ts and generate:api npm script
- Generate types into src/lib/api/generated/types.gen.ts
- Rewrite src/lib/types.ts as bridge with re-exports and augmentations
- Fix null vs undefined mismatches in consumer components
- Remove unused manual type definitions from api.ts
- Update AGENTS.md docs with type generation workflow

frontend/package.json

@@ -11,10 +11,12 @@
     "check": "svelte-kit sync && svelte-check --tsconfig ./tsconfig.json",
     "check:watch": "svelte-kit sync && svelte-check --tsconfig ./tsconfig.json --watch",
     "lint": "eslint .",
-    "format": "prettier --write ."
+    "format": "prettier --write .",
+    "generate:api": "cd ../backend && uv run python -c \"import json; from main import app; print(json.dumps(app.openapi(), indent=2))\" > ../frontend/openapi.json && cd ../frontend && openapi-ts"
   },
   "devDependencies": {
     "@eslint/js": "^10.0.1",
+    "@hey-api/openapi-ts": "^0.94.0",
     "@internationalized/date": "^3.11.0",
     "@lucide/svelte": "^0.561.0",
     "@sveltejs/adapter-node": "^5.0.0",