Both of the studies need to be reproduced and expanded upon in my opinion.
The MIT study is interesting, but controlling for the same task doesn't make sense to me. If you had two students doing a math test where a calculator mattered. One student had a calculator, and the other student didn't, I think you'll probably measure a similar difference in brain activity. But what the calculator does is enable the student to offload basic arithmetic so that they can focus on other concepts. For example, if one student was taking a test in which the calculator was useful but other types of mathematical problem-solving is necessary, and another student was doing arithmetic by hand, the brain activity probably would be similar.
You can use AI tools like a calculator, saving you from thinking about a sub-task and abstracting it away (although you probably should still check the output, due to hallucinations), while focusing your thinking on cognitive tasks that the AI can't (yet) help with. The college essay-writing scenario, just isn't one of these workloads. LLM's are pretty good at writing college-essays.
As for the second study, I would have to read the paper a bit more, but I think all that is shown is that there is a (moderate) negative correlation between simply using AI tools and lacking critical thinking skills. That's interesting, but not the same thing as "erodes critical thinking skills." You'd have to actually do some sort of cohort study, controlling for lurking variables (or a similarly designed experiment), to show "erosion." Simply showing that there is a correlation between people with less capacity to think critically and AI tool use, isn't enough. This is also probably why "education mitigates some cognitive impacts of AI reliance."
And that is only addressing the quantitative component. I am not convinced of the questionnaire methodology, which seems to be mostly based in self-perception.
I think the writer of the article also makes a good point,
"If survival in a technology-driven environment does not require the classical skills of human reasoning, those skills are likely not going to survive, fading from use like handwritten cursive, math without calculators, texting without autocorrect and books without audio."
Let's not forget that, these "classical skills" are actually pretty new in the grand scheme of things. For most of the history of the human species, humans lived as hunter-gatherers with a totally different skillset.