The "Multilingual App Toolkit" is not available in the Extension Manager for Visual Studio 2022 (yet). How can I build a project/solution that depends on this extension with VS2022? Without this support, I can't upgrade to .NET6.0 either, because that is no longer compatible with VS2019.
There's a workaround for this problem when VS2019 is installed together with the Multilingual App Toolkit for that version.
Simply copy the folder C:\Program Files (x86)\Microsoft Visual Studio\2019\Professional\MSBuild\Microsoft\Multilingual App Toolkit to C:\Program Files\Microsoft Visual Studio\2022\Professional\Msbuild\Microsoft\Multilingual App Toolkit. After this, VS2022 happily compiles projects depending on this extension.