What's the meaning of the Neo-Noir Spiderman's "APPLESAUCE" sound effect?

This is likely a variant of a fairly common joke in which a comic book fight with accompanying action words start out fairly mundane and slowly dial it up to 11, ending with a nonsense word that doesn't remotely resemble an acceptable sound effect. You can see almost the exact same joke in The Simpsons and a slightly more on-the-nose version in Bat Thumb.

The joke is a callback to Adam West Batman's slugfests, which tended to have unintentionally goofy effect words accompanying fight scenes with multiple villains against multiple heroes in a single open environment. Feel free to take your pick for examples, my favorite is ZLONK for punching somebody in the jaw or ZLORP for swinging into somebody on a chandelier.

Applesauce is a term of disapproval from the 1930s. It is a synonym for other words from the era such as malarkey or horsefeathers. It was also a term used to describe crooning lounge singer music. Basically all around it meant something mushy, weak, no substance, etc.

In this scene I took it to mean he defeated his opponent super easily, so it was a dig at the bad guy. Would easily combine with the other two answers here, as layers to the joke.