User management page on console throws error when adding user to a group

### Environment information

```plain text
System:
OS: macOS 15.2
CPU: (8) arm64 Apple M1
Memory: 267.70 MB / 16.00 GB
Shell: /bin/zsh
Binaries:
Node: 20.5.0 - ~/.nvm/versions/node/v20.5.0/bin/node
Yarn: 1.22.22 - /opt/homebrew/bin/yarn
npm: 9.8.0 - ~/.nvm/versions/node/v20.5.0/bin/npm
pnpm: 9.15.2 - ~/Library/pnpm/pnpm
NPM Packages:
@aws-amplify/auth-construct: 1.5.1
@aws-amplify/backend: 1.13.0
@aws-amplify/backend-auth: 1.4.2
@aws-amplify/backend-cli: 1.4.7
@aws-amplify/backend-data: 1.4.0
@aws-amplify/backend-deployer: 1.1.14
@aws-amplify/backend-function: 1.12.0
@aws-amplify/backend-output-schemas: 1.4.0
@aws-amplify/backend-output-storage: 1.1.4
@aws-amplify/backend-secret: 1.1.5
@aws-amplify/backend-storage: 1.2.4
@aws-amplify/cli-core: 1.2.2
@aws-amplify/client-config: 1.5.5
@aws-amplify/deployed-backend-client: 1.5.0
@aws-amplify/form-generator: 1.0.3
@aws-amplify/model-generator: 1.0.12
@aws-amplify/platform-core: 1.6.0
@aws-amplify/plugin-types: 1.8.0
@aws-amplify/sandbox: 1.2.9
@aws-amplify/schema-generator: 1.2.6
aws-amplify: 6.12.1
aws-cdk: 2.176.0
aws-cdk-lib: 2.176.0
typescript: 5.7.3
No AWS environment variables
No CDK environment variables
```

### Describe the bug

When adding a user created using social providers such as google or login with amazon to a group the console throws


Note: there are no errors when using Cognito console to add this user to a new group

### Reproduction steps

1. Signup with a social provider
2. create a new group using user management on console say `Admin`
3. select a user -> `Group membership`
4. then select the `Admin` group from dropdown
5. observe error

No source files or tests are named. Start by reproducing the console user-management flow with a social-provider user, create the Admin group, and inspect the group-membership operation when selecting it. Done means the user is added to the group without the console error, matching Cognito console behavior.

Written by the indexing model from the issue text.