waterwaymap only looks at things tagged as waterway= so all of the natural=water features are completely invisible to it. I’m sure there’s some extra preprocessing that could, for example, collapse all water= features to points so all of the in and outflows are “connected” but that requires features like w61823627 to get patched up as you suggest.
Setting aside that this area needs a redraw, I think it’s unusual to have waterways begin at the back of a water= feature. I wouldn’t say it is wrong just unusual for how folks map them. I don’t think connecting them up is wrong but it’s also not meaningfully more correct than leaving it disconnected. Honestly, I’d be tempted to delete those “originator” ways so the import seemed a bit more consistent with OSM “style”. But again, I don’t feel strongly about them.