In Procore, you can create two (2) separate lists of favorite tools in Procore. As shown below, you can create one (1) list for your favorite Company level tools and one (1) list for your favorite Project level tools. In addition, you can also create an 'across-project' list which you can apply to all of the Procore projects in your company account to which your user account has been granted access permission. See Create an 'Across Projects' Favorites List.
Company Level Favorites