US navy surface vessels have state of the art electro-optical sensors capable of taking very detailed photos and videos of airborne and surface targets.

These are used for both SAR and for target identification purposes you don’t want to blow up another civilian aircraft or a fishing vessel by mistaking it for with a military target.

I don’t know exactly what the US is running but sensors from other countries I’ve seen are capable of reading the tail number of a passenger jet from a substantial distance.

These sensors are also thermally stabilized and corrected for atmospheric disturbances as much as possible, and usually capable of visual spectrum + NIR and NUV to provide even higher fidelity.

If these sightings around carrier battle groups and fleets are indeed so common we should have pretty decent evidence of what these things are.