I haven't seen 也 used on its own for negation yet - is it a popular use? How does it work? Could you give more examples? 🙏
也 means even
你也配? (even you are worthy?) is a rhetorical question, it is in fact, a statement for "你不配" (you are not worthy)
(the standard hasn't sunk so low that even people like you are worthy/ qualified)
你配嗎? (are you worthy/qualified?) is another way to ask this rhetorical question. It too means "你不配" (you are not worthy)
三歲小孩也能當兵? (even a 3-year-old child can be a soldier?) is a rhetorical question, the answer/ statement is "of course a 3-year-old child can't be a soldier"
All of the above express the same meaning: you are not qualified (for something or to do something). Of course sentence a. is the most straightforward option. I'd say sentences b. and c. are rhetorical (hence the lack of negation), with sentence c. being much stronger than b., bordering on irony. We should not look at sentence c. as a statement (陳述句), but an interjection (感嘆句).
The dialogue would make better understanding if a question mark is included, as, 你也配？, which actually questions someone's "qualification or worthiness" rather than affirming it.
Saying, 你也配？ ( "You are qualified / worthy"?) rather than, say, "你配吗"?, ("Are you qualified / worthy"?) which unmistakably questions the worthiness, is what's called a "positive irony", a positive statement which carries a sarcastic implication of a negative meaning.
Your question, "Why is 也 used for negation of 你也配?"
也 here would mean "could also be considered as being..."
Thus 你也配? would be read in extended form as "You could also be considered as being qualified / worthy"?, which actually reinforces the positive ironic effect.
Actually without the 也 as "你配?" works just as well in the dialogue in question. I suppose the 也 is also for dialectic emphasis.
In here, 也 means "too", or "also".
For example - 那些人都是英雄. (你算老幾,) 你也配!? "All those people are heroes. Who the hell you are that thinking of yourself qualifies as one too!?"
你也配 is a frequently used phrase when one wants to show contempt for somebody's qualification/capability to be a character of high quality through a negative tune of questioning.
Another example - 她是個知書達理的大美人. 你也配!? "She is a classy lady with rarely seen beauty. Do you also have the qualities to be one!?
This use of 也 is for emphasis. Other examples: