ApiGatewayDeployment.make_auto_deployable does not account for API Stage Variables

Stage variable updates will cause an API Gateway UpdateStage call during SAM API stack deployment. However, since API Stage variables are not considered as hash input to ApiGatewayDeployment.make_auto_deployable, an update to a SAM API Stage can be made without a new deployment.

https://github.com/aws/serverless-application-model/blob/17000c195d65a41ee830173e7110ad2c36078a7a/samtranslator/model/apigateway.py#L95-L103

This means

1. The API Stage variables updates are not 'deployed',
2. UpdateStage will reset the Active API Deployment to it's last known good API Deployment ID. **If you have made other non-SAM managed deployments since your last SAM managed deployment, a latest change with just API Stage Variable changes will revert the active deployment Id to the last known good deployment**. This effectively reverts your latest changes made outside of the SAM managed changes.

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My team uses scripts to adjust the API Resource Policy (to onboard new clients), then deploy those authz changes using create-deployment, The above issue 2) recently caused an issue where our latest onboarding Resource Policy changes were no longer active after an API Stage Variable only change SAM deployment

REPRO:
1. Deploy SAM Api
2. Manually update the API Resource Policy
3. Manually deploy the API
4. Update SAM definition to add / change an API Stage Variable
5. Deploy the updated SAM definition

OBSERVE:
1. Step 5) creates an CFN Changeset with the update to the API Stage variables.
2. Processing that change set produces a Cloud Trail UpdateState Event where you can see both the new variable details, ,but also the 'reset' of the deploymnent value to something old.

IMPACT:
Your manual policy update step 2) is no longer active.