I wish this helpful for you Your question is purely .NET-C#-ish (at least I assume you use .net c#). Refer to this answer, please. If you achieve your goal in some way via .NET, you can do it in an Azure function - no restrictions on this side of the road. For sure you will need an external third-party library that somehow simulates a web browser. I know that Selenium in a way uses browser "drivers" (not sure) - this could be an idea to research more thoroughly.
I hope this helps you . If you use the developer feature of your web browser (Firebug, Inspector, Developer Tools, ...) you should able to see the connections being made to retrieve the data through Ajax and the request and response headers being sent and received. The request headers will contain the data being sent as well as the URL that's been request. The query string of the URL or the POST data would most likely contain a "start" or "next" or some time of parameter that identifies the start and number of results to return.
Scraping data from all asp.net pages with AJAX pagination implemented