more comments after committing the CL to CQ:
Line 349:
I think the code is fine, but think the explanation could be better... maybe something like this:

We want to call final_callback exactly once. When offliner->Cancel() returns false, the callback isn't called, so we call |callback| iff Cancel() returns false.

Line 361:
Run() has a r-value reference override, which presumably is a bit more efficient:
https://cs.chromium.org/chromium/src/base/callback.h?q=base/callback&sq=package:chromium&dr=C&l=132

so I would do std::move(callback).Run(...)