fix: separate durable async invoke flow

[reedham-aws]

Which issue(s) does this change fix?

There's not an issue, but a bug introduced in #8590.

Why is this change necessary?

Before this change, the "Event" type invoke for durable functions and on-demand functions had been mixed together. The issue is that this results in the durable execution header not being properly returned asynchronously. This broke some of our tests as well as not being the correct experience.

How does it address the issue?

Separate the flows. Durable functions already had its own asynchronous flow that was being preempted by the added one.

What side effects does this change have?

Should only effect durable functions, and should return the flow to the way it was before #8590.

Other note

When testing locally, I found that the sam-durable-function-emulator was still running after a test run. In a subsequent test run, this was causing failures unless I tore the container down manually. I also tested before any of these changes were added and confirmed that's existing behavior. That should probably also be fixed.

Mandatory Checklist

PRs will only be reviewed after checklist is complete

• Review the generative AI contribution guidelines
• Add input/output type hints to new functions/methods
• Write design document if needed (Do I need to write a design document?)
• Write/update unit tests
• Write/update integration tests
• Write/update functional tests if needed
• make pr passes
• make update-reproducible-reqs if dependencies were changed
• Write documentation

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