[proton0210]

Issue #, if available

Closes #4000. Thanks to @tiagohconte for the reproduction and proposed fix.

Description of changes

With MergeDefinitions: true, SAM writes ANY events under any instead of x-amazon-apigateway-any-method. It also drops generated routes when the inline paths is empty, null or missing.

Use the normalized method name for both lookup and write-back, and retain the paths dictionary in the merged body. Existing inline fields are preserved while SAM's generated integration takes precedence. Correcting the API body changes the deployment hash for affected templates.

Description of how you validated changes

• make pr on Python 3.12: all checks passed, 4,672 tests passed, 95.63% coverage.
• Eight new regression cases fail before the fix and pass afterward; a GET control passes in both versions.
• Transform snapshots cover missing/null paths and an existing OpenAPI ANY operation with CORS in all three partitions.
• An additional local audit passed 60 transform combinations covering method casing, Swagger/OpenAPI, five paths states, CORS and multiple events.

No live AWS deployment was run.

Checklist

• Review the generative AI contribution guidelines
• Adheres to the development guidelines
• Add/update transform tests
  • Using correct values
  • Using wrong values (unit regression for an invalid inline ANY operation)
• Add/update integration tests — covered by local transform tests; no deployed integration test added.

By submitting this pull request, I confirm that my contribution is made under the terms of the Apache 2.0 license.

[reedham-aws]

There is only one thing I'm concerned about in this PR: the existing case where a user has manually defined x-amazon-apigateway-any-method in the DefinitionBody while also providing an ANY method as part of the event source. Previously, that would have worked because of the value already in the definition body, while silently dropping what was in the event method. Now, the code is forcing the opposite and it's the manual DefinitionBody that is getting dropped.

I'm not quite sure what to make of this because it will change the behavior of existing templates, but at the same time that behavior was a bug. Theoretically, we can make the change, and then create an announcement mentioning that this might happen (not sure how many users would run into this).