ENH: Add JupyterLite-powered shell for the website (reprise of #47428) #47185

Job	Run time
ASV Benchmarks	23m 52s
Build Docker Dev Environment	2m 44s
Test install requirements-dev.txt	1m 43s
Docstring validation, typing, and other manual pre-commit hooks	16m 13s
	44m 32s

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