[OPS improvement] Stop syncing examples directory during release

### Describe the bug

The examples directory resides in the [Rust SDK examples](https://github.com/awsdocs/aws-doc-sdk-examples/tree/main/rustv1) in the `aws-doc-sdk-examples` repository, and there is no need to sync it in this repository.

### Regression Issue

- [ ] Select this option if this issue appears to be a regression.

### Expected Behavior

We should instead point customers to the [Rust SDK examples](https://github.com/awsdocs/aws-doc-sdk-examples/tree/main/rustv1).

### Current Behavior

N/A

### Reproduction Steps

N/A

### Possible Solution

_No response_

### Additional Information/Context

_No response_

### Version

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### Environment details (OS name and version, etc.)

N/A

### Logs

_No response_

Trace the release process that syncs the examples directory from this repository, then compare it with the Rust SDK examples in aws-doc-sdk-examples. Done means release synchronization no longer includes this directory and customers are pointed to the external examples repository.

Written by the indexing model from the issue text.