Thanks for posting your question in Microsoft Q&A, apologize for any inconvenience caused on this.
As from the details that you have mentioned in the thread it is clear that using the Microsoft documents you have configured according to them but please do double check the below points and if the issue still persists, please share the error screenshot or detailed error message that will help us in investigating the issue better.
Ensure that the Managed Identity is properly configured for the Logic App. This involves enabling the system-assigned managed identity and assigning the necessary roles, such as 'Storage Blob Data Contributor', to the Logic App's identity and also Confirm that the Managed Identity has the necessary permissions on the storage account. This can be set up in the Access Control (IAM) section of the storage account.
Also please note that the Azure Blob Storage managed connector has limitations, such as only being able to read or write files that are 50 MB or smaller. Ensure that your Logic App is not hitting these limitations, if you want to know that limitation, please do check the below document:
As per the documents mentioned it clearly states that if you're using the legacy trigger When a response to a Microsoft Defender for Cloud alert is triggered, your logic apps won't be launched by the Workflow Automation feature.
https://learn.microsoft.com/en-us/azure/defender-for-cloud/workflow-automation#supported-triggers
I hope the above provided information might help you, if you have any further queries, please feel free to reach out to us.
Thankyou.