Since moving to a self-hosted agent I did not have Powershell available or the bash command to parse JSON, jq. If you have installed Powershell onto your agents then please refer to this earlier post for my solution using Powershell: Using Powershell to Deploy a Logic App using an Office365 API Connection

Otherwise, I spent many hours working out how to accomplish the same with only Bash:

1. Validate then build the Office365 Connection

"resources": [
    {
      "type": "Microsoft.Web/connections",
      "apiVersion": "2016-06-01",
      "name": "[parameters('name')]",
      "location": "[parameters('locationName')]",
      "tags": "[parameters('tags')]",
      "kind": "V2",
      "properties": {
        "api": {
          "id": "[concat('/subscriptions/',subscription().subscriptionId,'/providers/Microsoft.Web/locations/',parameters('locationName'),'/managedApis/office365')]"
        }
      }
    }
  ],
  "outputs": {
    "office365connectionid": {
      "type": "string",
      "value": "[concat('/subscriptions/',subscription().subscriptionId,'/resourceGroups/',resourceGroup().name,'/providers/',reference(resourceId('Microsoft.Web/connections', parameters('name')),'2018-07-01-preview', 'full').resourceId)]"
    },
    "office365connectionname": {
      "type": "string",
      "value": "[parameters('name')]"
    },
    "office365endpointurl": {
      "type": "string",
      "value": "[reference(resourceId('Microsoft.Web/connections', parameters('name')),'2018-07-01-preview', 'full').properties.connectionRuntimeUrl]"
    }
  }

steps:
- task: AzureResourceManagerTemplateDeployment@3
  displayName: 'Validate ARM template'
  inputs:
    azureResourceManagerConnection: 'company-ais-dev'
    subscriptionId: '1xf291x0-0x61-4xx1-9097-777x44x1xxxx'
    resourceGroupName: 'rsg-company-dev'
    location: 'UK South'
    csmFile: src/Company.Azure.AIS.Common/Company.Azure.AIS.Common.Office365/azuredeploy.json
    csmParametersFile: src/Company.Azure.AIS.Common/Company.Azure.AIS.Common.Office365/azuredeploy.parameters.json
    deploymentMode: Validation
steps:
- task: PublishBuildArtifacts@1
  displayName: 'Publish Artifact: Company.Azure.AIS.Common.Office365'
  inputs:
    PathtoPublish: src/Company.Azure.AIS.Common/Company.Azure.AIS.Common.Office365
    ArtifactName: Company.Azure.AIS.Common.Office365

2. And the same for the Logic App container with the following app settings

{
...
            {
              "name": "WORKFLOWS_SUBSCRIPTION_ID",
              "value": "[parameters('subscriptionId')]"
            },
            {
              "name": "WORKFLOWS_LOCATION_NAME",
              "value": "[parameters('locationName')]"
            },
            {
              "name": "WORKFLOWS_RG_NAME",
              "value": "[parameters('resourceGroupName')]"
            },
            {
              "name": "OFFICE365_CONNECTION_ID", 
              "value": "[parameters('office365connectionid')]"
            },
            {
              "name": "OFFICE365_CONNECTION_RUNTIMEURL", 
              "value": "[parameters('office365endpointurl')]"
            },
            {
              "name": "OFFICE365_CONNECTION_NAME", 
              "value": "[parameters('office365connectionname')]"
            }
...
}

3. In the Release Pipeline I used the Office365 artifact and the Logic App container artifact



4. In the Release Pipeline Stage deployment, I do the following steps:
   
   Ÿ Retrieve some Key Vault secrets that are required
   Ÿ Deploy the Office365 connection and output the API details

   steps:
   - task: AzureResourceManagerTemplateDeployment@3
     displayName: 'Deploy Office365 Connection'
     inputs:
       azureResourceManagerConnection: 'company-ais-dev'
       subscriptionId: '1xx291x0-0x61-4xx1-9097-777x44x1xxxx'
       resourceGroupName: 'rsg-company-dev'
       location: 'UK South'
       csmFile: '$(System.DefaultWorkingDirectory)/Company.Azure.AIS.Common.Office365/Company.Azure.AIS.Common.Office365/azuredeploy.json'
       csmParametersFile: '$(System.DefaultWorkingDirectory)/Company.Azure.AIS.Common.Office365/Company.Azure.AIS.Common.Office365/azuredeploy.parameters.json'
       overrideParameters: '-environment dev'
       deploymentOutputs: connectionOutputs

   Ÿ Run a Bash script to save the output variables into pipeline variables to be used in the Logic App container deployment

   steps:
   - bash: |
      # Echo the API connection outputs JSON and format it using sed
      echo "$(connectionOutputs)"
      formatted_json=$(echo \"$(connectionOutputs)\" | sed -e 's/ //g'  -e 's/}/"\n}/g'  -e 's/{/{\n"/g'  -e 's/:/":"/g'  -e 's/,/",\n"/g'  -e 's/"}/}/g'  -e 's/}"/}/g'  -e 's/"{/{/g'  -e 's/\[/\[\n"/g'  -e 's/]/"\n]/g'  -e 's/"\[/\[/g'  -e 's/]"/]/g' -e 's/https\":\"/https:/g')                   
      echo $?
      echo "$formatted_json"
      
      # Extract values using awk
      values=$(echo $formatted_json | awk -F'\"value\":\"' '{for (i=1; i<=NF; i++) {print $i}}' | awk -F'\"' '{print $1}')
      echo $?
      
      # Convert the space-separated values into a bash array
      value_array=($values) #IFS by default is space
      
      # Print extracted values
      echo "${value_array[0]}"
      echo "${value_array[1]}"
      echo "${value_array[2]}"
      
      # Set Azure DevOps pipeline variables
      echo "##vso[task.setvariable variable=office365connectionid]${value_array[0]}"
      echo "##vso[task.setvariable variable=office365connectionname]${value_array[1]}"
      echo "##vso[task.setvariable variable=office365endpointurl]${value_array[2]}"
     displayName: 'Save API connection outputs to pipeline variables'

   Ÿ Finally, use the Office365 API connection outputs to create the connection in the Logic App container

   variables:
     office365connectionid: ''
     office365endpointurl: ''
     office365connectionname: ''
   
   steps:
   - task: AzureResourceManagerTemplateDeployment@3
     displayName: 'Deploy VLE Logic App'
     inputs:
       azureResourceManagerConnection: 'company-ais-dev'
       subscriptionId: '1xx291x0-0x61-4xx1-9097-777x44x1xxxx'
       resourceGroupName: 'rsg-company-dev'
       location: 'UK South'
       csmFile: '$(System.DefaultWorkingDirectory)/Company.Azure.AIS.VLE.LogicApp/Company.Azure.AIS.VLE.LogicApp/azuredeploy.json'
       csmParametersFile: '$(System.DefaultWorkingDirectory)/Company.Azure.AIS.VLE.LogicApp/Company.Azure.AIS.VLE.LogicApp/azuredeploy.parameters.json'
       overrideParameters: '-environment dev -office365connectionid "$(office365connectionid)" -office365endpointurl "$(office365endpointurl)"                  -office365connectionname "$(office365connectionname)"'

{
    "managedApiConnections": {
        "office365": {
            "api": {
                "id": "/subscriptions/@appsetting('WORKFLOWS_SUBSCRIPTION_ID')/providers/Microsoft.Web/locations/@appsetting('WORKFLOWS_LOCATION_NAME')/managedApis/office365"
            },
            "authentication": {
                "type": "ManagedServiceIdentity"
            },
            "connection": {
                "id": "/subscriptions/@appsetting('WORKFLOWS_SUBSCRIPTION_ID')/resourceGroups/@appsetting('WORKFLOWS_RG_NAME')/providers/Microsoft.Web/connections/@appsetting('OFFICE365_CONNECTION_NAME')"
            },
            "connectionRuntimeUrl": "@appsetting('OFFICE365_CONNECTION_RUNTIMEURL')"
        }
    }
}

...
   "connection": {
   "referenceName": "office365"
   }
...