This subclass really weaves together the bardic music and spellcasting, along with textile-related metaphors for music.

I think there's a "use", or some functionally equivalent word, missing in between "Whenever you" and "Tapestry of Song" in the Expanded Tapestry feature.

As far as balance goes, you're going to burn through bardic inspiration. Once it refreshes on a short or long rest, though, you're talking being able to buff the party around three times an adventuring day. That's probably not overpowered in and of itself, but I do worry that it tramples on one of the sorcerer's niches.