How much work could be got from temperature differences during a rocket's descent from low earth orbit?

The preferred answer is "as little energy as possible.". Reentery is designed with the expressed intent of minimizing heat transfer. The cargo inside universally prefers the high temperatures to stay outside. Such an engine would, by design, bring heat in, letting it warm the cold bath side of the Sterling engine.

As for how much energy could theoretically be harvested, that depends on the mass of the cold bath. Sadly, increasing mass is also the antithesis of what rocket designers aim for. Payload mass drastically limits our rockets. And, of course, all energy gained from reentery had to be put there by the launch rocket. Better to leave that fuel on the ground and burn it in a generator.

The one case you might get benefits is if you captured some very cold object that was on a near collision course with the Earth and diverted it towards a reentry.

If course, the political ramifications of this aren't simple. Major governments frown on plans to take a near miss of an asteroid like the one that killed the dinosaurs, and make it into a hit. Very unpopular