How is it subsidized while a local flight costs more than an international one?

The idea is to push people to use the train, but a train isn't an alternative if it takes 9 hours compared to the 2 hour flight.

ICE from Hamburg to Munich is about 5 hours. That's basically the other end of the country. Not sure where 9 hours come from.

And your 2 hour flight easily goes to 4-5 hours if you add the security theatre and the extra overhead that transport to/from the airport entails. They are far outside the city whereas central stations are usually in the city center.

What's the method of subsidy there? Contributing to Airbus shares?

Commercial aviation fuel is tax exempt in the EU, I would already count that as a subsidy (yes, I count not taxing something that's normally taxed as a subsidy, even if it isn't done by directly paying out money).

Subsidising airports and fuel, presumably.