Improve API Gateway documentation

Group traits by task (authentication, method/response, integrations,
endpoint and access control) and alphabetize within each group. Add
Validation sub-sections for traits with validators, cross-references
between aws.apigateway and aws.auth authorization traits, and a
section listing public traits from other namespaces that influence
API Gateway OpenAPI generation. Fix dead developer-guide links. In
the OpenAPI guide, expand the Other traits table, demote Cognito and
API key sections under Authorizers, and add a Recommendations section
covering jsonAdd, substitutions, and CloudFormation Fn::Sub patterns.

Author: mee-aa