Doesn't Debussy's Reverie sound like it is in Bb

Reverie is my favorite piece by Debussy. Don't get me wrong, Clair de Lune and his Arabesques are beautiful as well. But Reverie was my first real exposure to Debussy both as a listener and as a pianist. But I find something odd about it whenever I listen to it.

It is written in F major. However, to me, it doesn't sound like it is in F major except for a few moments and the ending cadence. The most well known part of it, the introduction, actually sounds like it is in Bb major to me. In fact this is 1 piece that I might consider to actually be in Bb Lydian since an Eb is so rare in this piece but it still sounds like the root is Bb. I hear a circle of fifths movement towards the middle of the piece where it feels like it moves from Bb to F and then later to C. Then it smoothly goes from C to Bb with no keys in between.

Does it sound like it is in the key of Bb to you? It certainly does to me, despite the cadence on F. Here is a video with the score.

At the beginning, I can see how you're hearing a sort of Bb6 tonality with the G's as opposed to a ii6/5 chord, but to me, when it gets to m. 9 it's pretty clear what's going on.