Up until now here in Germany we had a "system" that was a paper(!) card you put in your wallet if you were ok with donating your organs. That's obvioisly not an ideal system and Germany has far to few donors. We now moved to an online system and being Germany it's (as far as I've heard, I haven't tried it yet - which might be a sign that this is not going to be a great solution) is super complicated and convoluted. So basically even worse than the piece of paper in your wallet (seems impossible but for Germany business as usual when it comes to anything digital).
Personally this would be one of the very few things were I would be ok with something being opt-out instead of opt-in but I don't see that happening.
How weird that it's so different just over the border. Here in the Netherlands it's opt-out and afaik it was quite easy to enroll when it was still opt-in.
Apparently the paper card is still valid, there's the online thing and you can also put it in you advance directive(? that sounds made up, I mean "Patient*innenverfügung):