@Peter Thurwachter (MINDTREE LIMITED)
Apologies for the delay response here. Yes using those buttons does make API calls to calculate the size. However these same API calls are made whenever you load the blobs in the portal or Storage Explorer so you shouldn't see much affect on your bill. To test this you can open the container, wait some time then hit the calculate size button. Afterwards you can use the Insights tab under Monitoring to see how many and which API calls are made.
Hope this helps. Let me know if you have further questions or issues and I will be happy to help.
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