Does the Talmud teach a belief in the existence of the burning-forever kind of Roman Hell? Granted, I haven’t gotten far with the Oral side, but I haven’t seen that, yet.
The Jewish concept of punishment is as I have been taught a kind of 'purgatory' where the soul undergoes a painful cleansing process. Eventually, the soul returns to its maker afterwards.
The idea of a physical punishment of 'burning' is more of an anthropomorphized interpretation of a spiritual process. -Which is supposedly more painful than burning.
You're asking the wrong person. The afterlife is a relatively esoteric subject in Judaism (the thrust is on law). There are many Torah observant Jews on this forum who could answer your question far better than I.
There is the concept of "Ge'-Benei-Hinnom" (the valley of the sons of Hinnom, a reference to an area outside Jerusalem considered the worst place to live), but whether it is merely temporary and purgatorial for everyone or eternal for some I do not know.
“Does the Talmud teach a belief in the existence of the burning-forever kind of Roman Hell? Granted, I haven’t gotten far with the Oral side, but I haven’t seen that, yet.”
No, not really. Something unpleasant, yes. But it is reserved for the foulest of men, and perhaps none make the cut. Maybe Haman. Maybe Hitler. But then, Haman loved his children and Hitler loved his county and was very kind to animals. So hopefully not even them.
I will say that the Talmud contains the theology regarding the the world-to-come, and the Karaite approach of Torah only (first opined by the Sadducees as named in the Christian testaments) would mean that there is no world to come.
Such rejection of the Oral Law was specifically rejected by the original Christian founders, in that they specifically focused on the world to come.