ApiGateway: Docs do not describe what to depend on to wait for an API Gateway deployment to complete

I've done some testing, and it seems like one of the following 3 does what's needed, although this is difficult to absolutely confirm.
In the below, api is a SpecRestApi - https://docs.aws.amazon.com/cdk/api/v1/docs/@aws-cdk_aws-apigateway.SpecRestApi.html

someResource.node.addDependency(api)
someResource.node.addDependency(api.deploymentStage)
someResource.node.addDependency(api.latestDeployment)

Would it be possible to confirm what dependency should be taken to make sure that the resource will only be created after all API Gateway updates have been completed (like adding a new api path, or changing an integration configuration, or pointing to a new lambda).

Whatever the right approach is, could this be called out in the docs as this is something that consumers of this library will often want to do! For example - to run some validation tests which should not begin until the updates to the api are completed.

### Links

https://docs.aws.amazon.com/cdk/api/v1/docs/@aws-cdk_aws-apigateway.SpecRestApi.html

Start with the SpecRestApi documentation and compare the dependency behavior of api, api.deploymentStage, and api.latestDeployment for API Gateway updates. Confirm which dependency guarantees completion, then document that guidance and an example for validation resources; the existing API Gateway documentation link is the main entry point.

Written by the indexing model from the issue text.