You might want to have a look at the build-dir and keep-build-dir platformio ci parameters, since by default platformio ci uses a temporary build directory, and it is removed at the end of the build process. You can use those two flags to set it, and stop it from being deleted.
Now having said that, your last capture tells you where the platformio cache is … /root/.platformio/.cache … so if you want to used cached versions of libraries… cache that folder. Better yet, cache the entire /root/.platformio folder, and you should then have all the framework and toolchain files also.