I just posted a draft PR that implements the narrower fix:
https://github.com/python/cpython/pull/20287
I confirmed that the Django test passes with it. I also included two regression tests: one using only generators, and one more like the Django test that awaits a task.

My solution was to update the exception context in gen_send_ex() using _PyErr_SetObject() instead of _PyErr_ChainExceptions() -- because _PyErr_SetObject() does the cycle detection we've been discussing, and _PyErr_ChainExceptions() doesn't.

While _PyErr_SetObject()'s cycle detection isn't complete in that it can't detect cycles that begin further down the chain, it's good enough for this case.