The answer is yes, Animate object would work on a corpse. The exact effect would depend on the size of the corpse.
While there are specific defined terms in D&D 5e there are also a equal number of that rely on what the word means in English.
Object - a material thing that can be seen and touched.
Creature - an animal or person.
However there is a caveat. In various effects, powers, and abilities. The D&D 5e rules are consistent in referring to creatures as things that are living or animate. Objects as inanimate things like tables, chairs, rocks, books, feathers, etc. It not spelled out but it is consistent.
The things to remember is that D&D 5e rules are not to function as a wargame. They do not define the boundaries of what is possible during a campaign. The setting is what defines that. Instead they are a tool to aid the referee in adjudicating the action. For example the description of humans don't spell out every detail that could come up. The mechanics about humans are those that the authors feel that are useful or come up often. The important of which is the effect being human on character creation. The author expect referee to use what they know about humans to adjudicate anything that the rules don't cover because it is implied that humans in a D&D setting are just like people in real life only living in that world.
One implication of this is that animate objects doesn't change any other physical property of the object other than to animate with the stats provided. If you were to say animate a block of salt, possible considering what salt miners carved out of their mines, and it was to walk into water, then it is reasonable to rule that it would be affected adversely as salt dissolves in water. Perhaps by treating water as a acid attack on the animated object.
So a corpse animated as a object would still be a corpse and subject to decay, smelling bad, etc. It would not gain the benefits of being undead although at first glance it would be hard pressed for a character to tell the difference. One area where I can see the difference being important is trying to animate a skeleton. It is reasonable to assume that the various create undead spells joins the bones together to form a complete animated skeleton. While a long dead skeleton is merely a pile of separate objects of bone.
For stuff that has no real world analogue, elves, magic, etc. The authors expect the referee to fall back on their knowledge of the fantasy genre. Because the implied assumption that D&D is being used to depict a fantasy setting. Which is why they included a list of inspirational works in Appendix E on page 312.
In fantasy it is tradition for some spells to work on anything, a lightning bolt doesn't care if its target is a person, animal, or a piece of furniture. Some spells to only work on people, for example charming or enchanting a princess. And other spells to work only on objects, like the animated furniture from Fantasia.
Clever, but unlikely
In order for Catapult to work, it requires:
one object weighing 1 to 5 pounds within range that isn’t being worn or carried.
This is the requirement that Delayed Blast Fireball must meet. The question is: Does it?
Delayed Blast Fireball isn't explicit in the definition, but it does state:
A beam of yellow light flashes from your pointing finger, then condenses to linger at a chosen point within range as a glowing bead for the duration.
How much does a bead of light weigh?
In order for that bead to qualify for Catapult, it must be at least one pound and less than five pounds. As Dale M states, that's likely a DM call. But how should the DM approach?
Well, it's a beam of light that condenses into a bead. How much does a bead of light weigh? I'd think that a bead of magic light does not weigh anything, but another DM may believe otherwise. Then it's a question of does a bead of light weighs more than 1lb. Even if it did have a mass, it's unlikely to weigh more than 1lb.
Without meeting the weight requirement, you can't use Catapult to launch the Bead for extra damage (pending the save failure).
Throwing the Bead
There is another option for interacting with the Delayed Blast Fireball:
If the glowing bead is touched before the interval has expired, the creature touching it must make a Dexterity saving throw. On a failed save, the spell ends immediately, causing the bead to erupt in flame. On a successful save, the creature can throw the bead up to 40 feet.
This does imply that it can be handled, but it doesn't answer weight or anything else. Ultimately, this is a magic bead made of condensed light and it does not necessarily mean it has mass. It just means that you can throw the magic bead. If a DM does rule that it has mass, then it still needs to weigh more than 1 lb (see discussion above on weight of condensed light.)
Best Answer
Check with your DM
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 unofficial guidance is no rule, just a hint to help your DM deciding.
I think that because the item that you target with of Animating Performance is transformed into a creature1 and creatures other than objects cannot be "worn or carried", they only can be carried, you probably should check only at the beginning, when the item is an object.
The phrase "worn or carried" is used in many places in the rules to limit effects on objects in control of another creature, because otherwise many spells or abilities could act as a cheap trick to remove an opponents magic items or weapons. For example, it is used for the animate objects spell, that likewise turns creatures into objects. If you could suppress the effect by carrying, you just could grab an animated flying sword to stop the animation. That at least to me would be a very unexpected result. On the other hand, if you could just animate a sword your opponent is holding, it would be a cheap way to disarm them (and worse, directly use the weapon against them).
As a counterexample, telekinesis allows you to move only an object that is not being "worn or carried" automatically, and this limitation means you cannot just snatch their weapon out of their hands automatically. Instead, you need to make a contested Strength check to move it. Here I think it makes sense to always apply this, even if another creature later grabs an object you are moving, because the other creature now can counteract your movement.
So, when deciding to handle this phrase for ongoing effects, it makes sense to have the DM make a call that fits the specific context and situation.
1 The 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.