@Hannes Caesar Troubleshooting performance across multiple services is going to be tricky and ultimately, nobody here is going to be able to provide a clear solution. Opening a technical support ticket would put you in touch with someone who can see exactly what services are in play and use logs to understand the situation better.
With that being said, there are a few things I would suggest. You'll need to play around with your settings to see if anything yields a better result.
- Ensure both the fileshare and Web App (along with any other services) are all in the same region. This is the most common mistake. Note that West US and West US2 (or similar) are not the same data centers. These are geographically located at least 500 miles apart and this will introduce serious latency. All services should be in West US only for example.
- Play around with the size of the web app. S2 is good but try using a P1v3 for example. This is the latest architecture available. Using the higher tier for an hour or two will generate a little bit more in charges but you're billed per hour so the cost to scale up, perform your test, and then scale back down should be very minor. Just don't forget to scale back down.
- If none of the above solutions work, you can try using Azure Blob Storage instead of Azure File Share. Azure Blob Storage is optimized for storing and retrieving large amounts of unstructured data. You can use the Azure Blob Storage SDK for Python to read and write data to Azure Blob Storage.
Please let us know the outcome of the above steps.