Thanks for your replies and advices!

When Luna is done with her antibiotic treatment, her urine has to be tested again. I think my vet will discuss the option of a special diet with me when we get the result. I'm already feeding Hill's Indoor Cat, which supports the health of the urinary tract (she started eating it some weeks ago). Could be that she needs another food additionally. I will ask the vet for the products some have suggested here.

Luna seems to do fine this morning. She's playful and in a good mood. And she was a good girl and used her litter boxes during the night.

Kirsten