Sorry, I didn’t mean that one point to carry quite that much weight. I was quoting it only to make the limited point that nominative τρόπος can serve as a referent for adverbial τρόπος (and separately, unfortunately did not correct my confusing description in the original post quickly enough, as I see it quoted by you).
In the narrative flow here, I think that the unstated part, the part that’s assumed to be mentally present to the reader, is something like:
τρόπῳ τινὶ προσφέρει τὸ πρόσφορον τῇ τέχνῃ ῥητορικῆς.
With that sort of thing mentally present to the reader (maybe), and taking what is said as an answer to a question, I think we should understand copular ἐστί and translate something like:
Ὁ αὐτός που τρόπος τέχνης ἰατρικῆς ὅσπερ καὶ ῥητορικῆς.
It’s just the same (maybe) way for the art of medicine as for rhetoric.
With this understanding, we can see where the conversation is coming from and where it’s going. He’s talking about this way of providing the necessary that’s been asked about, and he’s now going to explain how it works in medicine.
However, I think that the gentle serve, return, return, return… of Platonic dialogue would get broken here by ἔστι of existence. That might be appropriate for a serve, but this is a return.
I saw your point about που meaning approximately, and while I don’t think there’s any language reason to choose the one meaning over the other (που just limits αὐτός, afaik), I think it wouldn’t be like Plato. “Approximately” would be a guarded but confident statement, like the unfortunate habit of modern Academize, but “perhaps” makes it a tentative but expansive statement, like Platonic Academize.