>> JupyterLab kernel

> There is no such thing.

A Web search reveals that the alternate term "Jupyter kernel," appears equally often. The terms are interchangeable.

> I'm pretty sure Sage was always intended as a project that integrates the world, never "small footprint".

A large install became true eventually, but it began as a small Python-based install, about 120 KB. Then people asked for extensions, and William Stein said "Yes".