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Xcode 13 minimum OS required is macOS Big Sur 11.3, Xcode13 can not be installed on this system(MacOS Catalina), you are right.
Visual Studio 2019 for Mac added support for Xcode 13 since version 8.10.10.8, Xcode13 and iOS15 SDK is necessary. If you just upgrade Visual Studio 2019 for Mac without updating XCode, I'm afraid you can't use the new features. You could keep the current stable version or upgrade it according to your business.
For more information, you could refer to https://learn.microsoft.com/en-us/visualstudio/releases/2019/mac/vs2019-system-requirements-mac
https://github.com/xamarin/xamarin-macios
Best Regards,
Wenyan Zhang
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