Set-AzConnectedMachineExtension_UpdateExpanded: The request does not have the mandatory extension properties in the body to perform the operation. Missing properties: Type

### Description

When using `Set-AzConnectedMachineExtension -ResourceGroupName 'RG-Example' -MachineName 'Example' -Name 'AzureMonitorWindowsAgent' -Publisher 'Microsoft.Azure.Monitor' -Location 'westeurope' -Type 'Microsoft.Azure.Monitor.AzureMonitorWindowsAgent'` I'm getting the error "Set-AzConnectedMachineExtension_UpdateExpanded: The request does not have the mandatory extension properties in the body to perform the operation. Missing properties: Type"

The error indicates that Type is required, and Type was provided.

### Issue script & Debug output

```PowerShell
DEBUG: 1:06:25 PM - [ConfigManager] Got nothing from [DisplaySecretsWarning], Module = [], Cmdlet = []. Returning default value [True].
DEBUG: 1:06:25 PM - GetAzureRMContextCommand begin processing with ParameterSet 'GetSingleContext'.
DEBUG: 1:06:25 PM - [ConfigManager] Got [False] from [DisplayBreakingChangeWarning], Module = [Az.Accounts], Cmdlet = [Get-AzContext].
DEBUG: 1:06:25 PM - [ConfigManager] Got nothing from [DisplaySecretsWarning], Module = [], Cmdlet = []. Returning default value [True].
DEBUG: 1:06:25 PM - [ConfigManager] Got nothing from [DisplayRegionIdentified], Module = [], Cmdlet = []. Returning default value [True].
DEBUG: 1:06:25 PM - [ConfigManager] Got nothing from [CheckForUpgrade], Module = [], Cmdlet = []. Returning default value [True].
DEBUG: 1:06:25 PM - GetAzureRMContextCommand end processing.
DEBUG: [CmdletBeginProcessing]: Starting command
DEBUG: CmdletBeginProcessing:
DEBUG: CmdletProcessRecordStart:

Confirm
Are you sure you want to perform this action?
Performing the operation "Set-AzConnectedMachineExtension_UpdateExpanded" on target "Call remote
'MachineExtensionsCreateOrUpdate' operation".
[Y] Yes [A] Yes to All [N] No [L] No to All [S] Suspend [?] Help (default is "Y"): A
DEBUG: CmdletGetPipeline:
DEBUG: CmdletBeforeAPICall:
DEBUG: URLCreated: /subscriptions/fc619802-fdfd-47ee-b4a6-4ff1529d5221/resourceGroups/REDACTED/providers/Microsoft.HybridCompute/machines/REDACTED/extensions/AzureMonitorWindowsAgent?api-version=2024-07-31-preview
DEBUG: RequestCreated: /subscriptions/fc619802-fdfd-47ee-b4a6-4ff1529d5221/resourceGroups/REDACTED/providers/Microsoft.HybridCompute/machines/REDACTED/extensions/AzureMonitorWindowsAgent?api-version=2024-07-31-preview
DEBUG: HeaderParametersAdded:
DEBUG: BodyContentSet:
DEBUG: 1:06:28 PM - [ConfigManager] Got nothing from [DisableInstanceDiscovery], Module = [], Cmdlet = []. Returning default value [False].
DEBUG: ============================ HTTP REQUEST ============================

HTTP Method:
PUT

Absolute Uri:
https://management.azure.com/subscriptions/fc619802-fdfd-47ee-b4a6-4ff1529d5221/resourceGroups/REDACTED/providers/Microsoft.HybridCompute/machines/REDACTED/extensions/AzureMonitorWindowsAgent?api-version=2024-07-31-preview

Headers:
x-ms-unique-id : 34
x-ms-client-request-id : 838d8338-51e6-46ee-9b60-cbfbe51167dc
CommandName : Set-AzConnectedMachineExtension
FullCommandName : Set-AzConnectedMachineExtension_UpdateExpanded
ParameterSetName : __AllParameterSets
User-Agent : AzurePowershell/v13.2.0,PSVersion/v7.4.7,Az.ConnectedMachine/1.1.0

Body:
{
"location": "westeurope",
"properties": {
"publisher": "Microsoft.Azure.Monitor",
"typeHandlerVersion": "Microsoft.Azure.Monitor.AzureMonitorWindowsAgent"
}
}

DEBUG: 1:06:28 PM - [ConfigManager] Got nothing from [EnableLoginByWam], Module = [], Cmdlet = []. Returning default value [True].
DEBUG: BeforeCall:
In progress [Checking operation status ]

DEBUG: ============================ HTTP RESPONSE ============================

Status Code:
BadRequest

Headers:
Cache-Control : no-cache
Pragma : no-cache
x-ms-operation-identifier : tenantId=33e01921-4d64-4f8c-a055-5bdaffd5e33d,objectId=82bfc4b4-118a-45b6-98a3-c5c30202027d/westus2/eebd7a57-1cd2-4b5e-88b2-38c56c415aed
Strict-Transport-Security : max-age=31536000; includeSubDomains
x-ms-request-id : 020a75da-2c5a-4353-be23-ff7c8f42a839
x-ms-ratelimit-remaining-subscription-resource-requests: 199
x-ms-correlation-request-id : a090c9b3-91a3-44bd-b1b9-f70a0a0a5b8e
x-ms-routing-request-id : WESTUS2:20250528T200634Z:a090c9b3-91a3-44bd-b1b9-f70a0a0a5b8e
X-Content-Type-Options : nosniff
X-Cache : CONFIG_NOCACHE
X-MSEdge-Ref : Ref A: 223742F0328646229AB08226086A6A38 Ref B: MWH011020807023 Ref C: 2025-05-28T20:06:33Z
Date : Wed, 28 May 2025 20:06:33 GMT

Body:
{
"error": {
"code": "HCRP400",
"message": "The request does not have the mandatory extension properties in the body to perform the operation. Missing properties: Type"
}
}

DEBUG: ResponseCreated:
DEBUG: BeforeResponseDispatch:
Set-AzConnectedMachineExtension_UpdateExpanded: The request does not have the mandatory extension properties in the body to perform the operation. Missing properties: Type
DEBUG: [Finally]: Getting exception 'Microsoft.Azure.Commands.Common.Exceptions.AzPSCloudException: InternalException' from response
DEBUG: Finally:
DEBUG: CmdletAfterAPICall:
DEBUG: [CmdletProcessRecordAsyncEnd]: Finish HTTP process
DEBUG: CmdletProcessRecordAsyncEnd:
DEBUG: CmdletProcessRecordEnd:
DEBUG: AzureQoSEvent: Module: Az.ConnectedMachine:1.1.1; CommandName: Set-AzConnectedMachineExtension; PSVersion: 7.4.7; IsSuccess: False; Duration: 00:00:08.4019677; SanitizeDuration: 00:00:00; Exception: InternalException;
```

### Environment data

```PowerShell
Name Value
---- -----
PSVersion 7.4.7
PSEdition Core
GitCommitId 7.4.7
OS Microsoft Windows 10.0.26100
Platform Win32NT
PSCompatibleVersions {1.0, 2.0, 3.0, 4.0…}
PSRemotingProtocolVersion 2.3
SerializationVersion 1.1.0.1
WSManStackVersion 3.0
```

### Module versions

```PowerShell
ModuleType Version PreRelease Name ExportedCommands
---------- ------- ---------- ---- ----------------
Script 4.0.2 Az.Accounts {Add-AzEnvironment, Clear-AzConfig, Clear-AzContext, Clear-AzDefault…}
Script 1.1.1 Az.ConnectedMachine {Connect-AzConnectedMachine, Get-AzConnectedExtensionMetadata, Get-AzConnectedLicense, Get-AzConnectedLicenseProfile…}
```

### Error output

```PowerShell

```

Start at the Set-AzConnectedMachineExtension entry point in Az.ConnectedMachine and compare its -Type parameter with the emitted request shown in the report. Reproduce the supplied command, then verify that the request includes the required Type property and completes without the HCRP400 error.

Written by the indexing model from the issue text.