Careful here. STEM definitely requires critical thinking, but crtical thinking is not just 'formal proofs', which is only useful when you're dealing with problems that are already obviously formalizable. This is not the case with the majority of problems in the humanities, e.g. history, literature, and large swathes of philosophy where data is qualitative.
Humanities majors are equipped with their own toolbox of concepts the same way STEM majors are equipped with theirs. For example, a philosophy major would learn important distinctions such as analytic/synthetic, extension/intension, descriptive/prescriptive, a priori/a posteriori, ontological/epistemological, type/token and so on. These are not concepts that you read once and remember and you've 'learned' them. It takes a lot of reading and writing and thinking and arguing over the course of years to grok. When done well, it can greatly illuminate a problem. Expressing the argument formally or in symbolic logic is usually a trivial exercise afterwards, the nature of philosophical inquiry puts the 'critical thinking' prior to the formal parts.
For example, consider the SEP article on Two-Dimensional Semantics: https://plato.stanford.edu/entries/two-dimensional-semantics...
The article is riddled with formal sections containing matrices and symbolic logic. But these are not the argument itself, and the people who came up with this framework did not arrive at this analytically through formal proofs. Rather, the formal aspects are only used to aid the intuition and remove ambiguity for readers. The bulk of the thinking requires creative and precise conceptual analysis that borrows and reinterprets a variety of well-trodden ideas in other areas of philosophy.
The more sociological and cultural departments of humanities probably have their own set of skills that are considered their versions of critical thinking. I imagine in cultural theory, one probably needs to know several interpretations of history to analyze their problems, since that fields literally deals with how historical baggage muddies the way we even define said problems to begin with. A STEM education, in a vacuum, is not going to be equipped with those tools. Why would they be? To think critically about cultural theory requires understanding facts that are embedded in its subject specific concepts. My ability to work through proofs in discrete mathematics is not going to be helpful here. But my ability to analyze history through say, systems of power is probably going to be necessary. That kind of thinking is missing from STEM, and trivially so -- it literally has nothing to do with STEM.
That is not a failure or criticism of STEM. That would be akin to criticizing English Lit departments for not engaging with math. But (and this is often the context "critical thinking" as a boon that the humanities offers is brought up) being able to recognize a politician's actions as bullshit is going to require more than just 'formal proof' -- it's going to require an ability to sort through social, historical, qualitative, ethical, and philosophical landmines. That ability is critical thinking.