Relevant quotes:
Enlarge. The target’s size doubles in all dimensions, and its weight is multiplied by eight. This growth increases its size by one category – from Medium to Large, for example. …
Animating Performance.
By 6th level, as an action, you can animate one Large or smaller nonmagical item within 30 feet of you that isn’t being worn or carried. …
I get the feeling that it doesn't since it's a temporary effect on an already animated object, but it was questionable enough that I wanted to check that I'm right against others' perspectives.
Best Answer
No it does not
Spells do what they say they do, because we have no real world experience to understand what they would do like for mundane things. Enlarge does not say anything about making its target inanimate, so it does not. Nothing in the spell description even remotely suggests it would make its target inanimate or non-magical or anything like that.
If your question is if an enlarged item counts as magical, and therefore would not be available to a later Animating Performance that only works on nonmagical items: the enlarged item does not become magical.
There are Sage Advice rules for what counts as magical: it is a magic item, the description says it is magical, it is a spell effect, powered by spell slots, or a spell attack. None of them is the case.
Enlarge does not say it turns the item magical, it is a not a magic item (unless it was a magic item to begin with), the item itself is not a spell effect (it only is enchanted by one), and neither is it one of the others fulfilled. Conclusion? Animating Performance will still work on it.
If your question is if the item becomes invalid because it now is too large to originally be targeted by Animating Performance, this is also not the case.
In general, the rules do not cover how to treat a target becoming illegal for an ongoing spell or effect, so this will be up to the DM. There is unofficial guidance that the effect would be suppressed while the target is illegal, but it does not apply in this special case: the item that you target with of Animating Performance is transformed into a creature1 and following that logic would mean the Dancing Item immediately reverts back to being a nonmagical, non-animated item because a creature is an illegal target for the initial effect, and thus the effect must be suppressed. Animating Performance would not work at all and that very clearly cannot be how this works. Instead, there can be no continual checking any more if the target still fits the description of being a "Large or smaller, nonmagical item" once animated. Thus, when you target the creature with Enlarge, the creature remains enlarged.
1The item, once animated by Animating Performance is not an object, it is a creature of type Construct. Enlarge works on both creatures and objects, so it will still work.
It probably would have been a bit clearer, had they said "object" instead of item, because that is a defined game term, but clearly they mean object by item here: "that isn't being worn" really would not apply to creatures.