Despite being a native speaker I'm afraid my knowledge of the Danish grammar isn't good enough to give you a definitive answer. But based on a bit of digging I think the cause of confusion is that "den"/"det" can both be a demonstrative pronoun, as in this exercise, or a definite article as in the scenario you're thinking of. And in the latter case the adjective would indeed take the same form for singular as it would for plural. So the following sentences are correct:
"Den kat er smuk!" = "That cat is beautiful!" (demonstrative pronoun: "den"/"that")
"Den smukke kat!" = "The beautiful cat!" (definite article: "den"/"the")
And a redundancy bonus: "Den smukke kat er smuk!" = "The beautiful cat is beautiful!"
Source (unfortunately in Danish): https://dansksiderne.dk/index.php?id=5034