Yep, indeed Hetzner. :)
I had tried that solution with a static route for the LAN segment via the Hetzner gateway before, but it failed because I added a route for the full LAN segment which was ignored / overridden by the LAN interface route. Stupid me. :)
After getting a hint in the Hetzner forum, I now added TWO static routes, one for the first and one for the second half of my LAN segment, and that worked nicely. Those routes were added correctly to the routing table, and since they are more specific (longer network mask) than the actual LAN route, they take precedence.