Writing the End of Deuteronomy

Hello. There is an assumption in the Gemara that the description of the death was not written by the same person (this is true for other individuals, see the issue there). You assume the HaBaZ, but from the Gemara it seems that he is not right. The Gemara only talks about eight verses, and there is no description of what was shown to Moses. This suggests that the Gemara truly believed that this description was still written by Moses and not Joshua, meaning that there is no prophecy here. But it should be noted that later on there is also a description of what happened to Moses and where he was buried, and if this was written by Joshua then it is still a prophecy. And yet there is a difference. First, Joshua’s description is purely factual and there is no problem with it being conveyed in prophecy. But to convey to Moses that he was going to die, when, how and where, is unlikely. Beyond that, there are descriptions of Moses’ greatness there, and even in this it is unlikely that Moses himself wrote (although it can always be said that he received instruction). And above all, there is a description there in the third person and it does not appear to be things that Moses himself writes. Apparently for this reason, according to the other method, Moses did indeed write a lament in tears (and the Graha explained: in tears, in a mixed manner).