[Python] Mitigate breaking changes for azure-mgmt-managementgroups

[msyyc]

[Python] Mitigate breaking changes for azure-mgmt-managementgroups

Summary

Fix Python SDK client naming for azure-mgmt-managementgroups TypeSpec migration.

Mitigation Applied

Breaking Change	Classification	Action
Client renamed from ManagementGroupsAPI to ManagementGroupsMgmtClient	Client Naming (#4)	MITIGATED via @@clientName

Change in client.tsp

Changed @@clientName(Microsoft.Management, "ManagementGroupsMgmtClient", "python") to @@clientName(Microsoft.Management, "ManagementGroupsAPI", "python") to preserve the existing client class name.

Accepted Breaking Changes (no mitigation needed)

Breaking Change	Category	Reason
CreateManagementGroupRequest properties de-flattened	#11 Flattened Properties	TypeSpec doesn't support multi-level flattening
CreateOrUpdateSettingsRequest properties de-flattened	#11 Flattened Properties	TypeSpec doesn't support multi-level flattening
HierarchySettingsInfo properties de-flattened	#11 Flattened Properties	TypeSpec doesn't support multi-level flattening
Deleted model AzureAsyncOperationResults	#7 Unreferenced Models	LRO result model not directly used
Deleted model EntityHierarchyItem	#7 Unreferenced Models	Unreferenced model
Deleted model ErrorDetails	#6 Common Types Upgrade	Replaced by common ErrorDetail
Deleted model ListSubscriptionUnderManagementGroup	#8 Pageable Models	Pageable wrapper model
Deleted model OperationDisplayProperties	#6 Common Types Upgrade	Replaced by common OperationDisplay
Deleted model OperationResults	#7 Unreferenced Models	LRO result model not directly used
15x params changed to keyword_only	#9 Keyword-only Params	Expected TypeSpec behavior

[github-actions]

Next Steps to Merge

Next steps that must be taken to merge this PR:

• ❌ This PR targets either the main branch of the public specs repo or the RPSaaSMaster branch of the private specs repo. These branches are not intended for iterative development. Therefore, you must acknowledge you understand that after this PR is merged, the APIs are considered shipped to Azure customers. Any further attempts at in-place modifications to the APIs will be subject to Azure's versioning and breaking change policies. Additionally, for control plane APIs, you must acknowledge that you are following all the best practices documented by ARM at aka.ms/armapibestpractices. If you do intend to release the APIs to your customers by merging this PR, add the PublishToCustomers label to your PR in acknowledgement of the above. Otherwise, retarget this PR onto a feature branch, i.e. with prefix release- (see aka.ms/azsdk/api-versions#release--branches).
• ❌ The required check named TypeSpec Validation has failed. Refer to the check in the PR's 'Checks' tab for details on how to fix it and consult the aka.ms/ci-fix guide

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