Does it need to be a key other than waterway=*? Judging from your post in the other thread, you seem to be concerned that renderers will blithely render any arbitrary waterway=* tag, but that doesn’t seem to be the case with any renderer I can find (other than the ones built into editors).
Also, I assume you’re only referring to the portions of the lake’s tributaries that extend into the lake artificially. By contrast, a river can logically flow through a reservoir, and the reservoir can be secondary to the river. But there might need to be a tagging distinction between a river that is digitized as artificial paths for rendering, those that go in a straight line for connectivity only, and those that are tagged more rigorously based on the thalweg or some other criterion.