There was some very recent discussion in the OSM forums for situations like this (where a river goes into a lake):

- "The end of the waterway map"
- https://community.openstreetmap.org/t/the-end-of-waterway-map/108632/14

Seems like some of the users came up with a newer tag:

- waterway=flowline
- https://wiki.openstreetmap.org/wiki/Tag:waterway%3Dflowline