It's also worth noting that FB doesn't need a lot of accuracy in the depth data for this to be "good enough" for a simple wobble effect on a phone.
It definitely doesn't need to be held to the same standards that would be held for a monocular depth estimator for, say, an autonomous vehicle or robot; in FB's case it doesn't matter whether the tree is 4m or 6m away, and really only matters that it's roughly behind the dog or cat or whatever.
Separately, depth estimators like this are also useful to fake the depth of field effects of large-aperture lenses, which I'm pretty sure is used on the latest Pixel and iPhone in their background-blurring "Portrait" mode; Facebook could quite possibly include that as an in-app feature to make such effects accessible to everyone with cheaper phones as well.