Can someone share insight about Debussy L.113 no.1 Doctor gradus ad Parnassum score?

I currently learn L113. no.1 taught by Claire. The score from download library has some discrepancy from other source. In the middle section of the piece (bar 37-44), key signature change to A-flat while many teachers (Claire as well) play in D-flat. I check many versions of scores most of them are in D-flat. However, there are some versions do publish in A-flat as well (Hal Leonard). Which one is correct? Do I miss something here? Can someone help me understand the harmonic function of that bridge section?

https://tonebase-emails.s3.amazonaws.com/Q2_2021/Q2W4/Scores/PNO/claire-huangci-teaches-debussy-childrens-corner-1-doctor-gradus-ad-parnassum.pdf