ENH: Add JupyterLite-powered shell for the website (reprise of #47428) #46724

Job	Run time
Build Docker Dev Environment	2m 36s
ASV Benchmarks	19m 57s
Test install requirements-dev.txt	1m 46s
Docstring validation, typing, and other manual pre-commit hooks	15m 37s
	39m 56s

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