If a project is licensed GPLv3 at top level but includes packages that are MIT, do the licenses of the included packages apply?
I understand your question like this: "I received the source code for a software package. The root directory of the source code contains a
COPYING file containing the GPLv3. I found a subdirectory in that tree that contains another project that has been re-used by the GPL project as sub-project. The subdirectory makes no mention of the GPL, but instead contains the MIT license. May I use code from that subdirectory according to the MIT terms?"
In that case, the answer is "most likely yes". The fact that the MIT-licensed code is re-used in an GPLv3 project does not change the license of that code. The MIT license still applies.
If the MIT-licensed source code has been modified by the authors of the GPLv3 project, they might think of their changes being licensed under the GPLv3. In my oppinion, they would have needed to adjust the license statement of the files they edited in case they don't want their changes to be subject to the MIT license. So, to be extra safe, you can try to receive the MIT-licensed source code from the original author instead of taking it from the source tree you have now.