`aws_api_gateway_integration` fails after changing endpoint method from GET to POST

After changing endpoint method type from GET to POST, `gradle deploy` fails.

Adding:
```
extensions {
terraform {
allowDestroy = true
```
to `build.gradle.kts` does not fix the issue.

Error log:
```
aws_api_gateway_deployment.root: Refreshing state... [id=zx6tdi]

Error: Cycle: aws_api_gateway_integration.users_find_user_get (destroy), aws_api_gateway_deployment.root, aws_api_gateway_deployment.root (destroy deposed 93f945ca)
```

Start by reproducing the failure with `gradle deploy` after changing the endpoint method from GET to POST, using the configuration in `build.gradle.kts`. Trace the `aws_api_gateway_integration` and `aws_api_gateway_deployment.root` resources named in the error and determine why the replacement creates a cycle; done means the deployment completes without the reported cycle.

Written by the indexing model from the issue text.