What are the major differences between PhD programs in mathematics and PhD programs in other STEM fields?
In brief, many aspects of math grad school are very different from CompSci, for example.

The vast majority of math grad students are funded by TA-ships, although some have NSF and other fellowships. The (large) size of typical math depts is tied to their role as service departments, teaching lower-division math, and this is what funds the large number of math grad students.

Internships in some applied math fields are desirable, but non-trivial to arrange.

Outreach and volunteer work are not strongly connected with these other questions.

It is not that math depts "disregard students' research interests", but that, almost universally in the U.S., further coursework beyond undergrad work is ... wise. If one has an unusually solid background, there are usually procedures by which to "test out" of requirements. On another hand, I am well aware that a certain number of grad students do feel that they're all ready to do research, and that coursework gets in the way. The "problem" is that "research" at a professional level in mathematics is not necessarily an immediate continuation of the sort of "research" typically done in undergrad projects. Another "problem" is that mathematics is an old subject, and there is a lot of very useful, helpful, enlightening stuff already known... and whose relevance to any given research project is very difficult to guess based on ignorance. I am absolutely not in favor of "oppressing" students by pointless busywork, but I am equally opposed to ignorance. Accurate perception of a given situation is difficult, and both students and faculty often have pre-existing biases... Again, testing-out of requirements ought to be a viable option, if one is well-prepared. If one doesn't see the relevance of the requirements, I'd tend to interpret this as reflecting a need to better understand the content of the required subjects. (Because they are relevant.)

In particular, depts to not "disregard students' research interests", except as not automatically exempting students from "requirements". Further, there are many hours in a day...

As to social events... it depends.

Networking? People know people. "Industrial connections" would exist only for very applied people, although connections to applied science research groups inside the university are common.

And/but none of what the question describes strikes me as unusually "uncooperative". In my observation, it is very common that math grad school is quite different from what people are expecting, exactly insofar as many students expect to immediately "start research" (perhaps parallel to the impression given about other STEM fields' programs), rather than having any required coursework at all. Also, there seems to be a not-uncommon disaffection with TA-ing, as though this were lowlier than having a fellowship of some sort or research assistantship... and is construed, again, as "obstructing research". But without all these TA-ships, many fewer math grad students would have any financial support at all. (There's little grunt-work available in mathematics that would compare to the low-level research-support work in some other STEM fields, which does (by tradition) get the student's name on a published paper, etc.)

So, yes, mathematics is somewhat different from other STEM fields. Further, the fact that a program is not what one presumed it would/should be is not at all a strong indicator that something's wrong with the program (although, of course, there are dubious programs). The greatest resentment I see is among students who believe that they're fully-fledged "researchers", and are offended to not be immediately treated as such... While this message can be imparted rudely, and perceived as "a rude shut-down", the many issues of professional competence are not easy for novices to judge.

(One more time: one can see about "testing out" of requirements...)

Edit: prompted by Brian Borcher's comment... Teaching is an important part of an academic mathematician's job! The question of "how much" is secondary. The TA experience is very important to get up to speed on teaching, and, in unhappy cases, to discover early on that one hasn't the taste for it, if that is so. (I had one PhD student who discovered this unhappy fact in his own case, so he did not take the academic route.) Part of what one should try to learn is that "teaching is not a burden"... !!! ... to say the least. :)