If you held the pedal for the whole bar it would make a mess. There's an F major for the first two beats, then a Bbmaj7 for the other two. All far too muddy. Yes, it may constitute Bbmaj7/F, but it's not good music. With a sostenuto pedal, it's quite feasible, and would work and sound good. But then the first F note would not be a quaver - it'd be a semibreve.
Maybe there's too much theoretical thinking going on. Please remember, theory came about as a way to explain what happened. It's not something to be adhered to, or even as a check-up on what's been played. That second chord is simply Bbmaj7, if you need a label.
And - we don't know what else is going on in r.h., so we're pretty well in the dark.