amplify init fails when selecting `sso-session` entry in profile list: `Failed to get profile credentials, Unexpected token A in JSON at position 0`

### How did you install the Amplify CLI?

npm

### If applicable, what version of Node.js are you using?

v18.16.0

### Amplify CLI Version

12.0.3

### What operating system are you using?

Mac

### Did you make any manual changes to the cloud resources managed by Amplify? Please describe the changes made.

No, I'm not even able to init.

### Describe the bug

Tryin to use Amplify with AWS IAM Identity Center. `amplify init --debug` fails with the following error:

```
Failed to get profile credentials
Unexpected token A in JSON at position 0

Learn more at: https://docs.amplify.aws/cli/project/troubleshooting/

ProfileConfigurationError: Failed to get profile credentials
at Object.getAwsConfig (/snapshot/repo/build/node_modules/@aws-amplify/amplify-provider-awscloudformation/lib/configuration-manager.js:939:15)
at process.processTicksAndRejections (node:internal/process/task_queues:95:5)
at async Object.run (/snapshot/repo/build/node_modules/@aws-amplify/amplify-provider-awscloudformation/lib/initializer.js:119:27)

Unexpected token A in JSON at position 0
ProcessCredentialsProviderFailure: Unexpected token A in JSON at position 0
at /snapshot/repo/build/node_modules/aws-sdk/lib/credentials/process_credentials.js:142:13
at ChildProcess.exithandler (node:child_process:411:7)
at ChildProcess.emit (node:events:513:28)
```

### Expected behavior

AWS nudges/recommends to use AWS IAM Identity Center. I would expect Amplify to be able to work with it. Is this not supported yet?

### Reproduction steps

The same behavior was reported by @josefaidt in https://github.com/aws-amplify/amplify-cli/issues/12174#issuecomment-1476927553

The issue says it's fixed, but I'm using the latest version and it's apparently not fixed.

Steps to reproduce:
1. `aws configure sso`
2. `amplify init`

This will fail with `Cannot read properties of undefined (reading 'accessKeyId')`.

3. Manually add `credential_process = aws sso login --profile ...` to `~/.aws/config`.
4. `amplify init` now redirects to SSO. After a successful login, the error above appears.

### Project Identifier

_No response_

### Log output

```
# Put your logs below this line

```

### Additional information

_No response_

### Before submitting, please confirm:

- [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.

Reproduce the failure with `aws configure sso` and `amplify init`, then compare it with the `credential_process` setup in `~/.aws/config`. Start at the `configuration-manager.js` and `aws-sdk/lib/credentials/process_credentials.js` locations shown in the stack trace; done means selecting an SSO profile lets initialization complete without the JSON parsing error.

Written by the indexing model from the issue text.