In Procore, you can create two (2) separate lists of favourite tools in Procore. As shown below, you can create one (1) list for your favourite Company level tools and one (1) list for your favourite Project level tools. Simply click the GRAY star in each menu, until it turns YELLOW.
Note: 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 Set and Apply Your Favourites Across Projects.