Maxperson
Morkus from Orkus
Arcane being the term associated with Wizardly magic and those other classes that access it in a variety of ways has long been established. It has been that way for most of the lifespan of D&D. That's not vague, it's just how TSR and WotC have decided it should be. The other side of that coin is divine magic, which includes nature and godly magic. Oaths are a subset of godly magic, as the vast majority of Paladins derive their power from the gods. Primal, a construct of 4e, seems like it would be a similar subset of nature and doesn't really need its own source name.The power source of the 5e Bard class is vague.
Only in the sidebox about the Weave, does the Bard get grouped with other classes that are "commonly" called arcane.
But this is in contrast to divine, that also lumps in Ranger. Divine includes gods, nature, oaths, and so on.
The bifurcation seems to only be a convenient generalization. It splits between sacred magic and secular magic. But actually there are a "variety of ways" to access the Weave, more than just two. This "common" oversimplification with regard to the Weave, omits discussions about psionic, primal, and other varieties of accessing the Weave.
The one that is different is psionics. That is a third way to access power and should have its own power source.
Those things don't talk about the power source, though. Those talk about how the Bard accesses the power source. Words of creation could be interpreted as divine. Or it could be interpreted as a type of wizardly magic or arcane. Unlike most other arcane casters, Bards do use cure spells, so I've always pictured them as having a bit of divine magic available. That fits into their schtick as jacks of all trades. Reshaping reality through music, though, is just a method of accessing the weave and doesn't warrant a new power source. Overall they are an arcane class with in my opinion, some dabbling into the divine. I don't see anything really psionic, but can see the logic in moving some of their abilities that way. If they dabble into the divine, why not into the psionic?The 5e Bard class description describes its own power source as the "words of creation". Both bards and the divine are using this same power source. "Words and music are ... vocalizations with power all their own."
Spellcasting: "You ... reshape the fabric of reality in harmony with your wishes and music." These kinds of descriptions that harmonize the wishes of the mind with fabric of the universe, connote what elsewhere is called Psionics.
The point is, in 5e, the power sources are vague. Any specific 5e setting has flexibility to assign whatever power sources make sense in that setting.