Java edition 1.17 won't start on Linux (GLFW error 65543)

When we try to start Minecraft we see a pop-up box saying:

GLFW error 65543: GLX: Failed to create context: GLXBadFBConfig.

Please make sure you have up-to-date drivers (see aka.ms/mcdriver for instructions).

and it won't start.

All packages are up to date (Debian stable).