@Michał Pawlicki
I am afraid that there is no direct way to see an activity log and check who modified/deleted/created files across the share. Azure Files currently supports Storage Analytics metrics, but does not yet support logging. There is already an existing feedback open for this. I recommend adding you voice here, this feedback and monitored by and responded to by Azure product teams. You can check the available monitoring scenarios here. However, most are in regards to capacity, the performance of the service and it´s health.
I hope this information was helpful. Please let us know if you have further questions or issues.
Edit:
Azure Storage logs in Azure Monitor is in public preview and is available for preview testing in all public cloud regions. Logging includes both SMB and REST operations. For more information please see Monitoring Azure Files.
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