You could create a new custom Folder content type then add "Project Manager" column to this content type.
1.Create custom content type.
Site Settings > Site content types > Create content type > Parent category select Folder Content Type > Content type select Folder > Create
2.Add column to this content type
In new content type page click Add site column > Create new site column > Remember enable Require that this column contains information
3.Add custom content type to your library.
Settings > Library settings > Content Types > Add from existing site content types > Select your site content types and click Add
4.My test result:
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