Hi @dnyandeo bharambe ,
I would look at using Azure Functions to leverage serverless and consumption scalability. Even logic apps are a viable option if all you're doing is basic data processing. So, you wouldn't need to process the file in SQL although you could; but I wouldn't unless there was an absolute need for it.
You can use a variety of triggers based on your needs; blob, timer, http. You can say for instance upload EDI files to a storage account through your API hosted in an app service or function app and have a separate BlobTrigger
function that will process the new data. Web jobs are another option that you can use but with functions, the platform will automatically scale out based on incoming request and load.
The link provided should get you started in the right direction but feel free to comment below if something doesn't make sense.