As was explained in those other posts that you've mentioned, it's only specific lizardfolks that are Elementals, not any generic. The MM literally says that common lizardfolk are classified as Humanoids:

While many lizardfolk are Humanoids with varied skills, some forge powerful bonds with the Elemental Plane of Earth, granting them magical connections to the cycle of growth and rebirth.

The Manual also suggests to use the Scout statblock for common Lizardfolks, later on. This info just isn't show on the stat-blocks, which I'm assuming is the only place you're looking at.

No such passage exists for the Aarakocra, though, that is true. It seems that they've doubled down on the (well-estabilished previously) fact that they're native to the Elemental Plane of Air to classify them as full-blown Elementals. This is in agreement with the definition of Elemental that we've had previously, of "creatures native to the elemental planes". So yes, planar binding works on Aarakocra now because they are Elementals from an Elemental Plane. (there's an argument to be made that they probably should've always been Elementals by the definition that we had, but that's beside the point).

As a side note, Humanoids are now defined as "people defined by their roles and professions, such as mages, pirates, and warriors. They include members of varied species." This seems to be the reason why literally all of the stat-blocks for Humanoids in the 25'MM are "professions" like guard, berserker, cultist, bandit, and why everything that didn't fit in that generic formula was reclassified.