It means that when the singer wakes up, you are there with him. It could also imply that you are the first thing he becomes aware of when he wakes up.

Oh dear, what a sad song...

Lyrics to songs can be sometimes tricky because there may be metaphors, imagery and symbolism but this one seems more interpretation friendly than others I've read. First the title COMATOSE helps to setup the meaning of the phrase. COMATOSE is when someone is unconscious. In other words, in a COMA. It appears the writer is describing life without the other person is "killing them" unless they have him/her in their life. "Waking to you is symbolic in the sense that he/she comes out of COMATOSE , like waking up from the dead but in the context of "waking next to you never felt so real" seems to suggest that even when the person is there, they are out if reach. You can try to Google the song and see if there are interviews with the song writer.

Not all pop songs are grammatical. Not all of them make sense. So one needs to judge carefully which ones deserve one's attention and which ones do not.

Hi :) Yes, the phrase "waking up to X" means that X is the first thing you experience upon waking. So, "waking up to you" means "you" is the first thing the singer is aware of after waking up. The "up" in waking up basically suggests a result to the action. It's not exactly the same as a perfective verb in Russian, but it's close. It's a very subtle difference, even for a native speaker. Also, you may have heard the phrase "wake up to yourself!", which we use to tell a person to become aware of their faults/situation.