[#15002] feat: add widget HTML type

[downstream-lean4]

This is the adaptation PR for leanprover/lean4#15002.

[downstream-lean4]

Build report for downstream: follow upstream PR

Turned red:

Repo	Critical	Build	Test	Lint
reference-manual	✅	⏭️	⏭️	⏭️
verso-web-components		🟥 in 36s	⏭️	⏭️

Stayed green

Repo	Critical	Build	Test	Lint
aesop	✅	✅ in 18s	✅ in 4s	⏭️
batteries	✅	✅ in 12s	✅ in 4s	✅ in 2s
import-graph	✅	✅ in 2s	✅ in 3s	⏭️
lean4-cli	✅	✅ in 3s	✅ in 0s	⏭️
mathlib4	✅	✅ in 1057s	✅ in 42s	✅ in 92s
plausible	✅	✅ in 3s	✅ in 2s	⏭️
ProofWidgets4	✅	✅ in 5s	✅ in 1s	⏭️
quote4	✅	✅ in 6s	✅ in 1s	⏭️
BibtexQuery		✅ in 3s	⏭️	⏭️
comparator		✅ in 3s	⏭️	⏭️
cslib		✅ in 34s	✅ in 8s	✅ in 3s
doc-gen4		✅ in 16s	⏭️	⏭️
illuminate		✅ in 8s	✅ in 11s	⏭️
lean4-unicode-basic		✅ in 4s	⏭️	⏭️
lean4export		✅ in 3s	✅ in 7s	⏭️
LeanSearchClient		✅ in 2s	✅ in 0s	⏭️
leansqlite		✅ in 9s	✅ in 20s	⏭️
repl		✅ in 4s	✅ in 59s	⏭️
verso		✅ in 129s	✅ in 88s	⏭️
verso-slides		✅ in 19s	✅ in 6s	⏭️

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