According to this documentation you need a basic service tier or higher to enable this feature. I have both a Standard tier and a Basic tier web app / app service. In both of them, the Application Insights blade (called Monitoring in this document) is greyed you, and when hovering I get the message "This feature is not supported for your current plan".
What does that mean? Neither this document nor the message tells me what's wrong or what the requirements are.
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@SWarnberg Thank you for the feedback! We are investigating this and will get back to you shortly.
@SWarnberg It appears that the documentation may be out of date. I'm assigning this to the document author to update accordingly.
@kobulloc-MSFT is there an ETA on this doc update? I'm having the same issue.
@EthanCo81 @SWarnberg Revisiting this, I'm unable to reproduce the issue that is being reported using an ASP.NET Web App on a B1 App Service Plan. Can you provide some more details about your setup to help us investigate this issue?

We're running our web app in a Docker container on Linux. I think someone said that it was the problem. If so, then both the documentation as well as the error message must be updated.
@SWarnberg Agreed. That error message is not as useful as it should be in identifying what the problem is.
@SWarnberg thank you for your patience on this one, I will get the docs updated today. I reached out to the engineering team to address the error message.
While we don't currently support auto-enablement of App Insights/Profiler via the UI for Linux based/containerized apps. There are some manual options which I believe are still in preview at the moment that you may want to look at:
@MicrosoftDocs/azure-cxp-triage #please-close
its still greyed out
@Rakatashii codeless monitoring with Application Insights on Linux is not currently supported. So Application Insights being grayed out on a Linux based web app/app service is still expected behavior. However, code based monitoring with Application Insights is supported on Linux, but it requires manually modifying your code to take a dependency on the appropriate App Insights SDK. So for example to add Application Insights to an ASP.NET Core app running on Linux you would need to follow this doc: https://docs.microsoft.com/azure/azure-monitor/app/asp-net-core.
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@Rakatashii codeless monitoring with Application Insights on Linux is not currently supported. So Application Insights being grayed out on a Linux based web app/app service is still expected behavior. However, code based monitoring with Application Insights is supported on Linux, but it requires manually modifying your code to take a dependency on the appropriate App Insights SDK. So for example to add Application Insights to an ASP.NET Core app running on Linux you would need to follow this doc: https://docs.microsoft.com/azure/azure-monitor/app/asp-net-core.