Death in Venice reads almost like Aschenbach's biography—you know, if he were real. The narrator has access to Aschenbach's inner thoughts, but also has a lot of opinions about him, his genius, and also his weaknesses. In fact, part of the novella's irony (check out the "Tone" section for more on this) has to do with the way the narrator takes a critical distance from the events of the story.
So what does this mean for the narrator's omniscience, a.k.a. his or her ability to know what's going on in everyone's mind? Well, it's pretty clear that the narrator has privileged access to Aschenbach's most private thoughts and experiences. Think about the stranger god dream in Chapter 5—the narrator records everything in vivid detail. Whoever our narrator is, they are definitely up inside Aschenbach's brain.
But what about the other characters in Death in Venice? They—like Tadzio, for instance—appear to us the same way they appear to Aschenbach: We have no idea what's really happening in their heads. That's what we call our narrator's omniscience limited.