feat(ui): implement LocalizationProvider within Mosaic

[alexcarpenter]

Summary

• Wires @clerk/i18n into the Mosaic design system as a peer dependency
• Splits MosaicProvider.tsx into three focused providers under providers/: appearance-provider.tsx, localization-provider.tsx, and mosaic-provider.tsx
• Adds LocalizationProvider + useMessages hook — components pass a base message object and receive merged overrides from the nearest provider
• Adds i18n-registry.ts as the central type registry for all Mosaic UI message namespaces
• Wires up organization-profile.messages.ts as the first consumer (orgProfile AIO messages)
• Updates swingset (StoryEmbed, StoryPreview) to wrap stories in the new MosaicProvider tree

Stacking note

This branch targets carp/i18n (PR #8861). After that PR squash-merges to main, rebase this branch onto main before merging — the single commit here touches only packages/ui and packages/swingset, so the rebase will be conflict-free.

Test plan

• pnpm --filter=@clerk/i18n test — 104 tests pass
• pnpm --filter=@clerk/ui test — no new failures vs base branch (pre-existing failures in ConfigureSSO / OrganizationSecurityPage are unrelated)

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Project	Deployment	Actions	Updated (UTC)
swingset	Ready	Preview, Comment	Jun 16, 2026 3:53pm

1 Skipped Deployment

Project	Deployment	Actions	Updated (UTC)
clerk-js-sandbox	Skipped		Jun 16, 2026 3:53pm

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[alexcarpenter]

Suggested change

	<MosaicProvider
	localization={{
	overrides: {
	organizationProfile: {
	title: 'hello world',
	},
	},
	}}
	>
	<MosaicProvider>

Just demoing overrides in practice