I was wondering if the moon was close to full moon and whether it had any connection to Lupin's heavy sleep on the train.
TL; DR It was a full moon IRL, but not in the Potterverse.
The Hogwarts Express leaves London on the 1st of September every year. In 1993 -Harry's third year at Hogwarts- it was a full moon IRL, as you can see in this calendar.
Since the train arrives after dusk, Professor Lupin should have turned into a wolf in front of the kids. So the moon was in a different phase in the book's universe.
It may be that J.K. Rowling forgot to check the moon calendar, or maybe she did but couldn't rewrite the chapters in a satisfying way and decided to use an alternative moon calendar for her universe.
Otherwise she would have had to find a credible reason to postpone the train's departure date for this specific year only, or remove Lupin from it, which would have completely changed the first part of the book.
The best indications we have on this alternate calendar are Lupin's transformations periods. He took his first sick leave in early November of 1993, and had a number of those during the year. The only night we know for sure was a full moon is the 6 June 1994.
There are 278 days between the two nights and 278 = 9*29.5 + 12.5
So in-universe the first of September was probably a waxing crescent moon.
I first assumed a lunar cycle of 28 days, but it's closer to 29.5 on average.