~~I think whoever wrote it just used the wrong word because yes inertia is dependent on mass, not momentum~~

Okay I actually decided to check and I think it just a poorly written explanation of rotational inertia

A rotating spheroid will oblate when its centrifugal force generates enough ~~inertia~~ angular momentum to slightly flatten it out into a more irregular, elliptical shape.

If the shape also changes, this would mean distribution of that mass relative to the axis of rotation would also have changed, which if I'm reading this right, affects rotational inertia.

Inertia is the tendency of objects in motion to stay in motion, and objects at rest to stay at rest, unless a force causes its speed or direction to change. from Wikipedia

So they're kind of just saying that once it picks up enough rotational speed.

They are talking about Moment of Inertia. Inertia wrt to rotation changes with how they are positioned in reference to the spinning axis. Think slender bodies are easier to rotate compared to wider bodies with same mass. That’s what they mean when earth slightly flattens out its becoming less slender and more difficult to rotate

Earth’s natural satellite can serve as a valuable research partner in measuring the sun’s oblateness. This is due to a phenomenon known as “Baily’s beads,” which are the tiny flashes of light during an eclipse that occur as solar light passes over the moon’s rugged terrain of craters, hills, and valleys. Since satellite imagery has helped produce extremely detailed mappings of lunar topography, experts can match Baily’s beads to the moon’s features as it passes in front of the sun.

The way I'm guessing this works is: Baily's beads will be detectable on shitty cameras since they will be distinct flashes of light, and since we have very detailed information of the moon's topography they can determine information on the sun based on your phone's location and the timing of the flashes of light.

And if that is how it works, that is fuckin rad. A+ science.