@MarkWoolaway-9275 As per my understanding from the description you have provided, you are looking for test automation frameworks for testing web applications. In my humble opinion, Azure automation isn't the service you are looking for. Azure Automation is mainly for process automation, configuration management, update management, shared capabilities, and heterogeneous features. Hybrid Runbook Worker feature of Azure Automation is to run runbooks directly on the machine that's hosting the role and against resources in the environment to manage those local resources.
If you have PowerShell script which automates your requirement to check the functionality of the web application then it is possible using Azure automation , however it isn't recommend for testing web applications.
If you are using Azure DevOps as your code repository, I would recommend to take advantage of Azure Test Plans for testing your web application which is suitable for your requirement.