To ensure the extension is installed, in Kudu, check the directory in D:\home\SiteExtensions\AspNetCoreRuntime.3.0.x64.
Once confirmed you can edit your web.config to point to the site extension as follows as a workaround
<aspNetCore processPath="D:\home\SiteExtensions\AspNetCoreRuntime.3.0.x86\dotnet" arguments=".\<project output>.dll" stdoutLogEnabled="true" stdoutLogFile="\\?\%home%\LogFiles\stdout" hostingModel="inprocess" />
See https://docs.microsoft.com/en-us/aspnet/core/host-and-deploy/iis/?view=aspnetcore-3.0#webconfig-file for more info.
It does seem this should be handled by the extension itself so there could be a problem there. Nonetheless, .NET Core 3 should be deployed in the next week or so as an available runtime.
EDIT:
You add the 'Use .NET Core' task in Azure Pipelines
to install the 3.0 SDK. This, in conjunction with --self-contained true --runtime <RID>
in the Publish task and <AspNetCoreHostingModel>OutOfProcess</AspNetCoreHostingModel>
in your csproj is an alternative to using the extension.