Bug: Durable execution experience with 'sam local invoke' is confusing and user unfriendly #9200

Description:

There are a couple of problems:

1. When you invoke a durable function without --durable-execution-name (or even if you do), the execution ARN is not printed anywhere. You have to run sam local invoke with --debug to even see it (but this can be incredibly noisy). For that matter, there's no SAM CLI to simply list local invocations. So the discoverability isn't good.
2. Even if you use --durable-execution-name, some of the other sam local commands (like execution history and execution get) do not seem to work with that name. There are numerous articles (probably AI written) on the Internet, as well as LLMs (I tried 2 separate ones and they both gave the same hallucinated answer) suggesting the opposite, but it doesn't seem to work for me. It's possible that those articles are entirely in error and it was only ever meant to take an execution ID. To be fair, the AWS docs (and the CLI help itself) are not particularly clear on this point.

Steps to reproduce:

• Build the app: sam build --beta-features --template path/to/template.yaml --build-dir .aws-sam/build/myfunc (in my case, I use --beta-features to get the python-uv build method enabled so I can use a pyproject.toml)
• Invoke the function: sam local invoke --template path/to/template.yaml --durable-execution-name test MyFunc --event path/to/event.json --region us-east-1. The function starts. In my case, there's a context.wait in the function to keep it alive.
• In a separate terminal run sam local execution history test. It errors saying: "Error: An error occurred (404) when calling the GetDurableExecutionHistory operation: Execution test not found"
• Cancel out of the function invocation and launch it with --debug. The execution ID is printed. Now run sam local execution history on this execution ID and it works.

Expected result:

Either:

1. The sam local invoke explicitly shows the execution ID somewhere in the output (without having to resort to --debug)
2. There's some new command or behavior in sam local execution that let's me simply list the executions in progress.
3. Allow --durable-function-name to automatically derive the latest execution

Additional environment details (Ex: Windows, Mac, Amazon Linux etc)

1. OS: Linux amd64
2. sam --version: 1.165.0
3. AWS region: us-east-1