This issue tracks the main "lift and shift" operation to move the material and cupertino libraries from the core SDK into their new, standalone packages in flutter/packages.

This is a critical, one-time migration of the entire source code for both design libraries. The goal is to successfully relocate the code into the new packages that have already been set up (#172938), connecting them to the new testing and release infrastructure (more in #172932).

This move is dependent on the completion of the prerequisite reinforcement (#53059) and Initial package setup (#172938).

Coordination and Cut-off

This action must be carefully timed to align with a stable release cut of the Flutter SDK. After the code is relocated and the new packages are published, the original libraries in the flutter/flutter repository will be closed to further changes. A clear "cut-off" point should be communicated, after which all new pull requests must be directed to the new packages.