When making a request to the Vision API Product Search an error occurs "message": "The request is missing a valid API key." - flutter

Question

When I register a service account for the Vision API Product Search there's a json file downloaded into my desktop that has the private key. However, when making a request into this api there's no place to send that JSON. I'll show you the documentation and my code.
I didn't understand also what is the curl request and how to send it using the http post request.
And This is my code:
Future<void> uploadProductSet() async {
var projectId = 'estoOne';
var locationId = 'europe-west1';
var url = 'https://vision.googleapis.com/v1/projects/$projectId/locations/$locationId/productSets';
final responseOne = await http
.post(Uri.parse(url),
body: json.encode({
'displayName': 'Product-Set-One',
}))
.catchError((error) {
throw error;
});
print(resoinseOne.body);
}

Answer 1

You have to send your access token with the Authorization header.
The API seems to use the Bearer authentication method.
So set the following header in your http request: Bearer $authToken
You should get the auth-token from the credentials file you've downloaded
So your code should look something like this: (untested)
await http.post(Uri.parse(url),
headers: { 'Authorization': 'Bearer $authToken' },
body: json.encode({
'displayName': 'Product-Set-One',
})).catchError((error) {
throw error
})