I booked a Berlin-Belgrade-Abu Dhabi-Sydney flight with Ethihad and due to a technical issue with the aircraft we didn’t fly out of Abu Dhabi until 13h later than scheduled.
The flight route (and ticket) originated in Europe, but the delayed flight leg did not. Am I due compensation under EU 261/2004?
As stated even on the web page you are linking to: Yes.
In October 2017, a EU Court of Appeal confirmed the UK CAA's interpretation that the final destination must be included in the total delay. This means that, if the passenger misses a connection outside the EU and ends up with a delay longer than the times indicated above, even if the delay on the flight leaving the EU was inferior to the aforementioned times, the total delay will be used and not only the delay on leaving the EU.
Relevant for the calculation of compensation is the delay on your final destination (the last stop on a multi-leg ticket).
There have been some disputes around this, since the wording in the regulation is not quite clear on this matter and several airlines have lately refused to pay compensation in such situations. In the latest relevant court verdict from October 2017, the UK Court of Appeal ruled however in two cases against Emirates that this is the correct interpretation of the regulation. There has previously been proceedings in other EU countries, where the courts have come to the same conclusion.
On 31 May 2018, the European Court of Justice ruled in Wegener v Royal Air Maroc, EU:C:2018:361, concluding:
the regulation applies to a passenger transport effected under a single booking and comprising, between its departure from an airport situated in the territory of a Member State and its arrival at an airport situated in the territory of a third State, a scheduled stopover outside the European Union with a change of aircraft.
It can't be much clearer than this that delays incurred at or after such a stopover are also covered by the regulation. (In Wegener's case, the ultimate cause of the passenger's delay happened at the EU airport -- but the court's reasoning does not even refer to this fact, and the conclusion is simply that the entire booking is covered by the regulation).
After much back-and-forth with Etihad themselves, and putting my case in the hands of one of the companies whose business is persecuting 261/2004 claims on behalf of passengers, it seems I am NOT due any compensation.
I believe the matter rests on the fact all delays occurred wholly outside the EU, on a non-EU carrier. If a delay had happened inside the EU (or possibly on an EU carrier) that had led to a cascading sequence of circumstances leading to me arriving > 4h late I would have been eligible. But since neither of those apply, I'm not eligible.