Not everything requires an "interface".
This whole thing is bizarre. Prior to this sidebar in the 5e PHB, no setting other than the Forgotten Realms had a "Weave" or an analogous concept. What this sidebar does is retcon an FRism into other established settings. It's unnecessary nonsense that will only annoy existing fans of other settings.
It's also an interesting thing to think about within the context of the FR itself—outside of Faerun, the goddess Mystra isn't worshiped, acknowledged, or even known about and magic works differently (see wu jen in Kara-Tur and Sha'ir in Zakhara). So, does this weave affect them, and when Mystra gets kacked as she is prone to do, does that affect their magic as well? Did the Time of Troubles, the Spellplague, and whatever else affect the magic of these cultures where Mystra is unknown and not worshiped? If it does, then why is she unknown, not acknowledged, and/or not worshiped—if her influence on magic is so ubiquitous then why isn't the knowledge and worship of her equally ubiquitous? Is this even addressed with the FR sourcebooks?