I agree that we can assume the writer is suggesting that back pain is a likely outcome of sleeping in a very small space.
I'm not completely averse to beginning that sentence with "But" (some people will say it shouldn't be used this way).
I would have simply run on the sentence as "... about the size of a phone booth but you don't have to worry ...", or I would have split it into two sentences and started the second with "However" - "... about the size of a phone booth. However, you don't have to worry ...".
Student or Learner