Replace nbconvert preprocessors by myst-nb preprocessors

[maximlt]

Currently notebooks are internally executed by nbconvert, but later parsed by myst-nb to support myst-markdown. Using myst-nb all the way would simplify the build process and would certainly come up with some more features and faster builds. What ties nbsite to nbconvert is mostly a few notebook preprocessors (e.g. removing the first n cells of a notebook output). myst-nb seems to have recently added support for preprocessors, it would be interesting to explore whether there would be a way to replace the current nbconvert preprocessors by myst-nb preprocessors. Interesting links:

• Allow preprocessing of NotebookNode executablebooks/MyST-NB#360
• https://docs.kai-tub.tech/common-nb-preprocessors/intro.html