The backend is almost entirely custom, though many common low-level open-source components are used pervasively. For example, for components written in C++ we use Abseil, Google Test, etc.
The SDKs are all open source and make use of other open source components:
You can find language specific libraries for many popular languages under the GoogleAPIs org on GitHub. To install, go to the defacto package manager for the specific language.
I'm interested in learning about Firestore architecture and how it solves difficult problems to understand and trust it. I'm not interested in client libraries.
The SDKs are all open source and make use of other open source components:
For example, the iOS SDK uses LevelDB for local key-value storage and gRPC for communication with the backend.