I think the crux of this issue is the ambiguous grammar of the clause
weave a performance into a basic spell
I can see two interpretations of this fragment.
- "I have a performance, and a basic spell, and I'm weaving them together".
- "I have a performance, and I'm weaving together different pieces of the performance to create a basic spell".
I think you're using the first interpretation, based on your phrase "have spells to which Arcane Art would add effects". However, I think the second interpretation is the one intended by the authors, as it feels like it clicks better with the feel of the rest of the system.
Based on the second interpretation, I'd say it definitively doesn't require any multi-classing. This ability to turn music into magic distinguishes a true Bard from a mere minstrel.