ENH: Add JupyterLite-powered shell for the website (reprise of #47428) #46744

Job	Run time
ASV Benchmarks	18m 58s
Build Docker Dev Environment	2m 43s
Docstring validation, typing, and other manual pre-commit hooks	15m 48s
Test install requirements-dev.txt	1m 42s
	39m 11s

Provide feedback