I might be misremembering but I feel like the Hamburg Regional Court did pop up multiple times because of legally questionable decisions in recent years.
No, the Hamburg court is well known for playing fast and loose with everything copyright or everything personal rights. They create jaw dropping rulings all the time, and quite often are reversed in part or fully by a higher court.
The Oberlandesgericht Hamburg was particular known for a Richter with the name Buske. He was well know for his "interesting" rulings. It went so far that IP/copyright/personal rights/media lawyers coined the term "Buskeismus" (Buskeism). He is retired since about a year, but his spirit seems to still live on especially in Hamburg's courts.
Yes, they will get the chance to argue in front of a higher court. But they can't skip the lower court.
If I understand it correctly (Quad9 is a bit sparse on details here), this was a decision to uphold the original injunction. This decision is open to immediate appeal to a higher court, but Quad9 will have to show that there's an especially high urgency for that. Otherwise they will have to wait for the judgment in the principal case.
The Oberlandesgericht Hamburg was particular known for a Richter with the name Buske. He was well know for his "interesting" rulings. It went so far that IP/copyright/personal rights/media lawyers coined the term "Buskeismus" (Buskeism). He is retired since about a year, but his spirit seems to still live on especially in Hamburg's courts.