So the survey done last year in Asia — during the twilight of the Bush era — found the US was rated very highly in “soft power” even in Muslim Indonesia.
If so, then what is the damage Clinton is supposedly repairing? There is a fundamental contradiction there.

China's autocrats have always hated Democrats, and favoured Republicans.
Bush handled the Chinese very well…which requires skill. Note his blunt lecturing them on human rights in August…which they were happy to swallow as he balanced it with his presence at the Beijing Olympics…which was a major compliment in Chinese eyes.
Of course, Bush got no credit for that.

Clinton wanders aimlessly about…reading between the lines: getting up late, and not being on time for anything…and she gets (artfully qualified) praise on the front page of the WaPo.

Also, to echo Greenschemes: Huh?

Why did no one hear of this survey last year…when everyone confidently declared the US despised in the rest of the world because of Bush?

Seems now that wasn't really the case.

Why did the WaPo not put it on the front page then?

This cannot be. Everyone knows that everyone hated the George Bush led USA.