This PR changes the format check on CI to use the command added in
https://github.com/flutter/engine/pull/50747.
Additionally, while making this change, I noticed that the CI check was
not checking the formatting of all files, and that as a result, files
were present in the repo with incorrect formatting. I have fixed the
formatting and fixed the check to always check all files.
## Description
This turns off the Doxyfile option `CREATE_SUBDIRS` because it prevents deep link URLs from being stable. It means that thousands of files will be in the main directory, but the filesystem should be able to handle that.
I got rid of the header/footer files for doxygen (because Doxygen will generate them anyhow) and fixed where it was looking for the Flutter logo.
I also ran Doxygen on the Doxyfile template and Doxyfile and updated all the options to correspond with the latest Doxygen.
