Closes https://github.com/flutter/flutter/issues/160257.
~~This will sit on CI for a bit and give me a better idea of how much
work there is to do.~~ Done!
## IMPORTANT: Do **not** revert on 1-2 isolated post-submit failures.
While I've spent the last several weeks getting this passing all
presubmit tests, and some integration tests I suspected might be
affected, it is possible that there are 1-2 integration tests that will
fail as a result of landing this PR. I'll disable the flag
(`--no-explicit-package-dependencies`) if the failures look obvious
enough, otherwise I'll revert.
043b71954c