Since this is around 600m long, you can argue that it should be tunnel=flooded ("an artificial structure intended to channel water on a significant distance" "(over 100 meters)" – see https://wiki.openstreetmap.org/wiki/Tag:tunnel%3Dflooded ) rather than tunnel=culvert, and I would be fine with that too, but what is clear is that this needs SOME tunnel=* tag because it runs underground.