Hi Frederic,
Welcome to Microsoft Community.
I'm Hahn and I'm here to help you with your concern.
It seems like your Surface Book 3 is experiencing an issue where the USB-C port is not properly recognizing your external drive, and the discrete GPU (RTX 3000) also disappears when the drive is not detected. The fact that both the drive and the GPU are recognized after detaching and reattaching the display or when using the Surface Dock indicates a potential issue with the connection between the base and the tablet portion, or possibly with how the system manages the USB-C port and the GPU when attached.
USB-C ports can handle both power delivery (PD) and data transfer. If your external drive requires a specific PD profile or power level, the Surface Book 3's port might not be providing enough power. On the other hand, the Surface Dock is designed to provide enough power to the connected devices, which can be confirmed by the fact that your external drive works fine.
Since your device is Surface Book 3 for Business (owned by an organization), see Surface service options for Business and Education.
Sincerely hope that your question will be dealt with appropriately after contact the correct department. Thank you for your understanding!
Your Sincerely
Hahn. W - MSFT | Microsoft Community Support Specialist