Hi, @Ingmar Crone
Listening to your scenario (accessing many JSON files with API), I came up with the idea of using Cosmos DB.
If you haven't considered it yet, consider adding authentication to Web API and storing backend data in Cosmos DB.
https://azure.microsoft.com/ja-jp/services/cosmos-db/#overview
There are other options.
You can also store the JSON file in Azure Storage and access it via API.
If you can't achieve the scenario with Cosmos DB, you probably have more requirements. Please tell them.