How to interpret the value of categorical cross entropy?
There is usually no straightforward interpretation of what cross-entropy means in the context of the given task. In practice, it is more important to follow the trend of how the cross-entropy develops during the training.
The measure comes from the information theory. It says how surprised the model is when it has some belief about the output (a distribution) and you provide it with the ground truth output. A nice (but not very useful) interpretation is that the entropy of $x$ means the same surprisal as observing an output of rolling and $2^x$-sided dice.
The value of cross-entropy indeed depends on the number of classes, just because with more classes you have the output distribution must cover more options and it is more difficult to assign more probability to the ground truth class.