“I half expected the Stoics to say we should just get by on our own, with nothing but reason to guide us and to spurn any offers of emotional support.”

This is precisely the issue I had with stoicism when I first learned of it. It nearly turned me off completely. Often when the philosophy is presented in popular media it comes across as a philosophy for emotionless, atomistic automatons. I’m glad I found enough interesting in stoicism, however, to read more. Like you point out, particularly with Seneca, it’s clear that the popular understanding of stoicism as merely the philosophy of suppressing emotions is wrong. For me stoicism recognizes emotion as natural but provides a practical philosophy to curb the more debilitating, long-term effects of unbridled emotion. It’s also, as A Year of War and Peace argues, a philosophy that’s big on community and cosmopolitanism.

Unfortunately, I think your implicit argument here is correct: the messaging and presentation of stoicism, some notable exceptions aside, is woefully horrible. Too often it’s presented as no more than the mantra: “suck it up, bro.”