Can you estimate how much cargo a ship is transporting by measuring how tall it is compared to the sea? Is this something that would be feasible with a constellation of tandemSAR-like satellites?

Wow, that's a cool idea. I bet you absolutely can. When you image a ship broadside, it gets projected onto the surface in a flattened way we call "layover" - here's an example of how nicely ships pop out on a flat sea: https://x.com/umbraspace/status/1797970305798816030

Depends on the ship as well, not all ships change their draught ("depth") that much according to what they carry, but ships like bulk carriers and oil carriers certainly do. They report it via AIS data as well, but as its manually input it is often unreliable. An other idea that has been utilized is to look at the vake patterns (wave patterns) to estimate the speed of the ship.

Does the commercial tasking feed into the open dataset? Or is it more a case of once the satellite is up, might as well keep it busy?

Just wondering since the distribution of locations shown in the blog post seems particular.

It's cherry-picked, but it's a combination of commercial tasking and discretionary tasking. There isn't much to read into in terms of the distribution, it's just one person's best guess at where there's likely to be a lot of diverse types of ships.

This is really interesting. I have worked a lot with AIS data (messaging system that relays information such as the position of a ship), but the AIS data can some time lack information (and sometimes can be spoofed). However I have never got around working with imagery data. This seems like a great starting point for that :)