The data in the NBC article you posted is Texas specific and runs through 2022. The MMWR report you cite is aggregate data that runs through 2021. It isn't a gotcha. It's a pretty simple question. Where is the detailed description of the methods and results of the research you cited?
Maybe it does, maybe it doesn't.
What I see in the crude rate charts is an increase from 2019 to 2020, and from 2020 to 2021, followed by a decrease from 2021 to 2022. The Texas abortion ban went into effect Sept 1, 2021. So 2022 is the only full year data under that policy. Overall 2022 rates are lower than both the 2021 and 2020 rates. The race/ethnicity segments are interesting, but the demographic segment with the lowest pre-2021 abortion rate has the greatest increase in maternal mortality. The race/ethnicity segments with the greatest abortion rates pre-2021 have much lower increase in maternal mortality rates. Pretty obvious this doesn't hang together, which is why I was sincerely interested in the analytical methods that led the "researchers" involved to their conclusion as you framed it: "Covid played a part, but these researchers said Texas’ abortion ban is the main reason behind Texas’ quintupling the national increase." COVID is probably driving the raw numbers. You suggested this was teased out in the analysis, but I don't see that. Probably a straightforward difference in differences analysis with some reasonable covariates would suffice. Doesn't have to be overly complex, "Algebra works fine" isn't really how this actually works unless you are in 7th grade math class.