Use the `rust-launch` from the the docs repo (#3240)

## Motivation and Context
<!--- Why is this change required? What problem does it solve? -->
<!--- If it fixes an open issue, please link to the issue here -->

## Description
<!--- Describe your changes in detail -->

## Testing
<!--- Please describe in detail how you tested your changes -->
<!--- Include details of your testing environment, and the tests you ran
to -->
<!--- see how your change affects other areas of the code, etc. -->

## Checklist
<!--- If a checkbox below is not applicable, then please DELETE it
rather than leaving it unchecked -->
- [ ] I have updated `CHANGELOG.next.toml` if I made changes to the
smithy-rs codegen or runtime crates
- [ ] I have updated `CHANGELOG.next.toml` if I made changes to the AWS
SDK, generated SDK code, or SDK runtime crates

----

_By submitting this pull request, I confirm that you can use, modify,
copy, and redistribute this contribution, under the terms of your
choice._