You asked below whether my other comment in this thread (from December 2018) supports your comment here. My sense is that it does. "I have to go sleep now" to me clearly suggests that you are going somewhere. "I have to go to sleep" seems to suggest that you want to fall asleep. Exactly where you fall asleep is unspecified.
I am not a native German speaker - probably speak German at a high B2 - so I provided a link in my other comment explaining why the German sentence does NOT mean "fall asleep."
Here's an explanation I found with a quick Google search. I hope it helps.
My ESL students often ask about the difference between "I will do this" and "I am going to do this." Both are future tense. I was interested to learn that "going to do" is a fairly recent development in English. Shakespeare used "going to + verb" only when someone was literally going somewhere.
To me, there's something similar with "go to sleep" - which often means "fall asleep." I don't think this is the case in German. "Schlafen gehen" seems to mean leaving one place and then sleeping in another.
"I have to go sleep" definitely does not mean "I have to sleep right here, right now... snore." It does mean that "I am leaving to go sleep somewhere." That seems to match salivanto's "leaving one place and then sleeping in another." Whereas, "I have to go to sleep" says nothing about where... I might very well say that to a traveling companion before dozing off in my airline seat until the person behind me starts kicking it.