There are a couple of options.
Reacting to Azure Blob storage events | Microsoft Docs
An Azure Logic App could also trigger and for example queue an event on a storage queue or event bus:
Connect to Azure Blob Storage - Azure Logic Apps | Microsoft Docs
Or you could do polling yourself to look for new data.
There is a lot to balance (speed, cost, complexity) and unfortunately not a single "best solution for everything", so you need to dig in and find an acceptable solution for you.
Be careful when Microsoft states you only pay for what you use. As developer, this typically makes us think "I only pay if something happens", but in the Microsoft world, it might be a fixed monthly cost for just having the ability to run something - unfortunately I never found a fast way to tell the two apart without extensive reading.