Adding a linked file to the project doesn't copy the file to that project. If you run the project from Visual Studio, any page which references the linked CSS file won't be able to find it.
If you publish your project, the linked file should be copied to the output folder. If you then run the published output, it should work.
If you want the same file to be physically present in both projects so that you can see it when you debug, you would need to create an OS-level link instead.
Hard Links and Junctions - Win32 apps | Microsoft Docs[
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