Map fonts from a different folder on server

Font Mapping isn't what you think it is. Regardless, there's no such preference for accessing a specific folder for fonts.You SHOULD install the fonts locally; the System wants that.

Some 3rd party Font Managers have Server versions, which can deal with remotely stored fonts; serving them to all users within the license you paid for. Maybe that's your best approach.

Other than that, you can store fonts within the InDesign's Application Font folder, although that makes them only available to InDesign, so why do that. Also: When you package a document to send to someone else, this creates a Document Fonts folder along with the document, which InDesign will look in for missing fonts not on your system, but this is document specific, so really, not what you're looking for.

Regardless, sharing fonts is a legal conundrum unless you have a multi-seat license anyway.

Although it is possible to upload your own fonts to your CC account (through Manage Fonts), you would need an Enterprise CC to share them amongst a team beyond your own CC account.