.NET Core is flexible regarding different versions running on the same web server.
Publishing an application as self-contained, will allow you to run as many different versions as you would like on the same web server. See .NET Core application publishing overview.
Only if you are publishing as framework-dependent would you need that specific .NET Core runtime installed on the web server. And even then you can publish applications with different versions, as long as the runtime is installed.
Different from .NET Framework, you will see that your Application Pool will have "No Managed Code" for the .NET CLR Version.
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