I mean, Hanbalis are Atharis, that's an undisputed fact, so much that "Athari Aqidah" and "Hanbali Aqidah" are synonyms. If you want to say the 4 madhab are ahlul sunnah, you have to include the Hanbalis, and thus you have to include the Atharis. ibn Qudaymah, one of the leading and most influence Hanbali scholars, declared all of the Asharis outside the fold of Ahlul Sunnah. You will never find one single Hanbali who will ever disavow Shaykh ibn Qudaymah.

And really Athari Aqeedah is the only real link between people like ibn Uthaymeen, al Shawkani, and al Albani, not much is similar, each had a different madhab in fiqh. You can't simultaneously have your cake of "traditional islam" and eat it too.