the api with id doesn’t include a route with path

In Console, manually:

• I have created a lambda based authorizer, java implementation with events APIGatewayV2CustomAuthorizerEvent, SimpleIAMPolicyResponse. I have tested it and know that it works.
• I have created an API Gateway then attached this authorizer. When I make a call it always return 401 and doesn't call my authorizer (it has to write to log).

Looks like the issue based on wrong permissions: when I open tab "Triggers" on function's page it shows attached trigger "API Gateway" with message

The API with ID bk???1e doesn’t include a route with path /* having an integration arn:aws:lambda:us-east-2:11???37:function:my-authorizer.

Another lambda is integrated with this API Gateway, also manually with Console and this pair works as expected: if I detach my authorizer all calls go from the Gateway to the integrated lambda.

Also I have found some materials on re:Post and Youtube and they look outdated:

• now Console doesn't have options "token" and "parameter" authorizers, I can choose only JWT and Lambda, and for Lambda authorizer I can choose Payload version 1.0 or 2.0
• there isn't the button "Test" for authorizers