Hello Ross Keeling
Thank you for your question!
The error about "no storage option" or "no supported storage option for this configuration" suggests a problem with the setup of the diagnostic settings or the target destination.
Firstly, please be informed that Azure File Shares are typically hosted in a Storage V2 account. If you are using a Storage Account (General Purpose v1), you may not have access to certain logging features.
However, to enable diagnostic settings for your Azure File Share Select Your Storage Account: Find and select the storage account that contains your Azure File Share. In the left-hand menu, scroll down to the Monitoring section and click on Diagnostic settings. Click on + Add diagnostic setting. 
In the diagnostic settings, you should see options to select logs and metrics. Ensure you check the boxes for File Share logs and metrics.
Regarding cost increase since you are using the hot access tier, ensure that you are not inadvertently moving data to a cooler tier, which could incur additional costs. Check if there are any unexpected data transfer charges, especially if you are accessing the file share from outside Azure.
References: https://learn.microsoft.com/en-us/azure/storage/files/storage-files-monitoring
If this doesn't work, please help me the error snip of "no storage option" or "no supported storage option for this configuration" and confirm us Which guide are you following when setting up logs for your Azure File Share? to investigate further and provide you the best solution.
Please use the comment section if you have any question or concern, we are happy to assist you.