[WIP] Align to Docsy theme

[lmktfy]

Redo the custom theme to be closer to vanilla Docsy.

Here's a preview

ℹ️ Derived from PR #48363

Helps with issue #41171

/area web-development

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This PR is too large to merge as-is.

/hold
until it is small enough to be reviewable as a single change (eg size/XL or smaller)

I will continue to carve off smaller PRs that are reviewable.

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[lmktfy]

I'll rebase this when I get a big enough moment.

[lmktfy]

Broke out a change; see PR #51832

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