Main problem with german law is that the courts have too much freedom because they know, the lawmakers produce low quality laws nowadays.
Just compare any old law with any of the newer ones… Germany is losing it, sadly.
Is that just me?
But it costs time, money and should not be necessary.
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.