chore(test): move invoke/start-api/start-lambda durable function test to unit test

[roger-zhangg]

Which issue(s) does this change fix?

Why is this change necessary?

There's no Durable function test coverage in unit test, causing
#8608 #8590 unknowingly broke Durable function.

How does it address the issue?

Move few DAR test from integ test to unit test.

What side effects does this change have?

N/A as we still have other DAR test coverage in integ test

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.

[roger-zhangg]

Integ test: https://github.com/aws/aws-sam-cli/actions/runs/21765301977
DAR test failure is expected. We have another incomming PR to fix it

[bchampp]

Thanks!