NickDiaz-9048, To better assist you on this, could you please share more details on what Azure service you're leveraging? (The website is hosted on an Azure VM? or it's an Azure App Service WebApp? Or you're leveraging Azure Communication Service for your requirement).
Typically, you would implement/have code written (OTP generation modules) similar to as you would on on-prem/or any platform, on Azure.
On Azure Communication Service, refer this doc -How to Get Started with Azure Communication Services Part 2 of 2 - Send SMS messages.
-You may take a look at this doc and discussion thread1, thread2 for some pointers.
PS. We will have to add/adjust additional tags, so you can receive insights from the targeted audience.