Even with an extremely low resolution radar hit they are very identifiable.

Most naval vessels move in groups/squadrons. Carriers basically always travel with a "carrier strike group"/CSG of a dozen other ships and destroyers often travel in "destroyer squadrons"/DESRONs. So any time you see a cluster of hits, just by the relative responses of each hit you can narrow down and guess the entire CSG/DESRON in one go and then work out which responses map to which ship in the CSG/DESRON once you have a good idea of which group you are looking at.

This is especially true because ships even within the same class have varying ages, different block numbers, and differing retrofits. So each one has a unique signature to it.

But also if you aren't completely certain you can always come back with a second high resolution pass and then it's trivial to identify each ship just visually.

> I would think

Just do a youtube search and you'll find plenty of talking head explainer videos. Ignore the talking head and just look at the imagery and data they share.

SAR operates in side-looking slant geometry.

Consider shooting a ray at the ocean at an oblique angle from a satellite: it bounces off and scatters away from you. Hardly any of the energy scatters back towards you.

Now, put a ship there. The ray bounces off the surface of the ocean and scatters up into the side of the ship, and from geometry, it's going to bounce off the ship and come straight back towards its original source. You get tons of energy coming back at you.

A ship on the ocean is basically a dihedral corner reflector, which is a very good target for a radar.

> I'm having a hard time imagining a sufficiently high radar resolution for such a wide sensor swath width at such an extreme range. Is the idea that you locate it with the wide sensor swath and then get a detailed radar signature from a more precise sensor?

That's one approach, there are so-called "tip and cue" concepts that do exactly this: a lead satellite will operate in a wide swath mode to detect targets, and then feed them back to a chase satellite which is operating in a high resolution spotlight mode to collect detailed radar images of the target for classification and identification.

However, aircraft carriers are big, so I don't think you'd even need to do the followup spotlight mode for identification. As an example, RADARSAT-2 does 35 meter resolution at a 450 km swath for its ship detection mode. That's plenty to be able to detect and identify an aircraft carrier, and that's a 20 year old civilian mission with public documentation, not a cutting edge military surveillance system. There are concepts for multi-aperture systems that can hit resolutions of less than ten meters at 500 km swath width using digital beamforming, like Germany's HRWS concept.

tl;dr: Radar works very well for this.