An ellipsis in dialogue indicates an unexpected pause or silence or trailing off. (While dashes indicate a sudden break or interruption.)
Since "What?" and "What!" are complete utterances, it is hard to interpret "What?..." or "What!..." because we expect the punctuation to be the end of the sentence. I suppose it might be interpreted as a puzzled expression or desire to say something more, but the speaker is struggling to think of what to say. In that case, I'd write that in exposition. Gary looked like he wanted to say more, but struggled to find the words.
I don't think using "!..." is a shorthand that conveys that properly, it is just confusing and will break reader immersion.
"What...?" is a more reliable method, it indicates the questioner asked "What" and intended to elaborate but was at a loss for words; so there was a pause, then a questioning expression.
Similar to a character talking to their mother, they might say "What the... What in the world are you talking about, mom?"
The reader will guess the character caught himself before saying "What the fuck" to his mother.
I can't think of a good reason to use an expression ending punctuation followed by an ellipsis. "!..." or "?..." or "[period]...". Laziness, perhaps.