Just came across this - https://www.karwansaraypublishers.com/awblog/war-elephants-in-north-africa/
Short, presumably the paywalled link referenced is more detailed.
I've seen the DNA evidence referenced before, and found the argument quite weak. The absence of forest elephant DNA in a modern bush elephant population doesn't seem to me to prove anything beyond reasonable doubt. Now find me the remains of an ancient elephant and extract DNA from that, and I might be convinced.
I do think that sometimes DNA evidence is taken to much as a silver bullet to answer questions. I assume that the paper referenced is more than just that, but I'm not so interested as to pay to read it ;)
Even if it were bush elephants the Carthies used, it hardly follows they were as large as modern bush elephants; different populations of the same species may differ quite a bit in size. Consider Dutch and pygmies.
Do I gather correctly that we have no Holocene elephant fossils from the Maghreb or Egypt? Given what else they got up to, it seems churlish of the Egyptians not to mummify any nellies for us.
It took too long to extract the brains through the nose, I guess
Cheers
Mick