Well, according to your own source, it depends.
The historical and accept use of Deep South includes east Texas. Then the article states: Today, the Deep South is usually delineated as being those states and areas where things most often thought of as “Southern” exist in their most concentrated form.
In mind mind, that most certainly includes Texas. But, maybe they’ve become more Yankeefied than I had believed. I suspect my Texan friends would take issue with you on that point.