Made the paddle a proper floating world object instead of just a static pickup lying around the scene.
The main thing was creating a dedicated convex hull mesh for the paddle. Buoyancy calculations work better with a simplified stable hull than the actual render mesh, so I made a separate low-poly version just for that. Then wired the paddle up to the NetworkFloatingMesh script and set the relevant scene configuration so it actually behaves as a floating networked object.
After that it was just tuning mass, submerged drag, angular drag, until it felt like something you dropped in the water rather than something teleporting around. The result is that if you drop the paddle it actually floats and you can recover it, which is the whole point of having it as a world object at all.