Deploy is stuck when frontend is skipped

### Before opening, please confirm:

- [X] I have checked to see if my question is addressed in the [FAQ](https://github.com/aws-amplify/amplify-hosting/blob/master/FAQ.md).
- [X] I have [searched for duplicate or closed issues](https://github.com/aws-amplify/amplify-hosting/issues?q=is%3Aissue+).
- [X] I have read the guide for [submitting bug reports](https://github.com/aws-amplify/amplify-hosting/blob/master/CONTRIBUTING.md).
- [X] I have done my best to include a minimal, self-contained set of instructions for consistently reproducing the issue.
- [X] I have removed any sensitive information from my code snippets and submission.

### App Id

https://ap-east-1.console.aws.amazon.com/amplify/home?region=ap-east-1#/d35bsvaicfsnob/pr-141/2

### AWS Region

ap-east-1

### Amplify Hosting feature

Console

### Frontend framework

React

### Next.js version

N/A

### Next.js router

N/A

### Describe the bug

I have these 3 variables set

in order to skip backend completely.

I created a pull request intentionally to test the case of updating a file outside of the frontend code folder (https://github.com/aitok-ai/LibreChat/pull/141), the result is that we successfully skip the building process but we got stuck for Deploy

Output of the Deploy phase

### Expected behavior

The deploy phase is skipped as well.

### Reproduction steps

1. create a PR that changes files outside the defined `AMPLIFY_DIFF_DEPLOY_ROOT` folder

### Build Settings

_No response_

### Log output

output of the Build tab
```
2023-09-18T05:01:39.533Z [INFO]: # Cloning repository: git@github.com:aitok-ai/LibreChat.git
2023-09-18T05:01:43.293Z [INFO]:
2023-09-18T05:01:43.352Z [INFO]: Cloning into 'LibreChat'...
2023-09-18T05:01:44.158Z [INFO]: From https://github.com/aitok-ai/LibreChat
* [new ref] refs/pull/141/head -> pr-141
Switched to branch 'pr-141'
2023-09-18T05:01:44.193Z [INFO]: Successfully cleaned up Git credentials
2023-09-18T05:01:44.194Z [INFO]: # Checking for Git submodules at: /codebuild/output/src1132725565/src/LibreChat/.gitmodules
2023-09-18T05:01:44.200Z [INFO]: # Retrieving environment cache...
2023-09-18T05:01:44.523Z [INFO]: # Retrieved environment cache
2023-09-18T05:01:44.523Z [INFO]: ---- Setting Up SSM Secrets ----
2023-09-18T05:01:44.523Z [INFO]: SSM params {"Path":"/amplify/d35bsvaicfsnob/prbeb/","WithDecryption":true}
2023-09-18T05:01:44.565Z [WARNING]: !Failed to set up process.env.secrets
2023-09-18T05:01:44.571Z [INFO]: # Determining if there are deployable frontend differences relative to repository root at: client
2023-09-18T05:01:44.571Z [INFO]: # NOTE: Set the AMPLIFY_DIFF_DEPLOY_ROOT environment variable to a valid relative path to override the default, ie: dist
2023-09-18T05:01:44.663Z [INFO]: # No differences detected.
2023-09-18T05:01:45.291Z [INFO]: No live updates for this build run
2023-09-18T05:01:45.296Z [INFO]: # Retrieving cache...
2023-09-18T05:01:45.356Z [INFO]: # Extracting cache...
2023-09-18T05:01:45.358Z [INFO]: # Extraction completed
2023-09-18T05:01:45.358Z [INFO]: # Retrieved cache
2023-09-18T05:02:08.905Z [INFO]: ## Skipping Frontend Build & Deploy, No changes detected...
2023-09-18T05:02:08.962Z [INFO]: ## Build completed successfully
2023-09-18T05:02:08.963Z [INFO]: # Starting caching...
2023-09-18T05:02:08.967Z [INFO]: # Creating cache artifact...
2023-09-18T05:02:08.969Z [INFO]: # Created cache artifact
2023-09-18T05:02:08.970Z [INFO]: # Uploading cache artifact...
2023-09-18T05:02:09.044Z [INFO]: # Uploaded cache artifact
2023-09-18T05:02:09.044Z [INFO]: # Caching completed
2023-09-18T05:02:09.046Z [INFO]: # No custom headers found.
2023-09-18T05:02:09.050Z [WARNING]: !! No index.html detected in deploy folder: /codebuild/output/src1132725565/src/LibreChat/client/dist/
2023-09-18T05:02:09.050Z [INFO]: # Starting build artifact upload process...
2023-09-18T05:02:09.066Z [INFO]: # Uploading build artifact '__artifacts.zip'...
2023-09-18T05:02:09.068Z [INFO]: # Uploading build artifact '__artifactsHash.zip'...
2023-09-18T05:02:09.166Z [INFO]: # Build artifact upload completed
2023-09-18T05:02:09.166Z [INFO]: # Starting environment caching...
2023-09-18T05:02:09.166Z [INFO]: # Uploading environment cache artifact...
2023-09-18T05:02:09.204Z [INFO]: # Uploaded environment cache artifact
2023-09-18T05:02:09.204Z [INFO]: # Environment caching completed
Terminating logging...
```

### Additional information

_No response_

Start with the Amplify Hosting deploy flow that handles AMPLIFY_DIFF_DEPLOY_ROOT and the “No differences detected” path; compare the Build and Deploy phases shown in the logs. Reproduce with a pull request changing only files outside client, then confirm that the deploy phase is skipped rather than attempting artifact upload.

Written by the indexing model from the issue text.