While Azure Log Analytics Workspaces supports access using a Managed Identity (formally known as: Managed Service Identity, MSI), the official Logic Apps connector for Azure Log Analytics (Azure Monitor Logs) does not.
Edit 2023-12-04: The Logic App connctor for Azure Log Analytics supports managed identities now. So the following workaround is no longer needed.
As a workaround queries to a Log Analytics Workspace can also be send directly to the Azure REST API, as the built-in HTTP connector in Logic Apps supports Managed Identities.
⌨️ Example
I have added a minimal example to my bicep-snippets repository: bicep-snippets/logicapp-msi-workspace at mother · manualbashing/bicep-snippets (github.com)