feat(ui): expose composed profile API via @clerk/ui/experimental

[alexcarpenter]

Stack 7/7 (top). Wires everything up: the composed barrel, the @clerk/ui/experimental flat named exports, the package.json/tsdown entrypoint, and the integration tests.

This is the only PR that changes the public surface — @clerk/ui minor. Merges the full composed UserProfile / OrganizationProfile API.

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Stack

#	PR	Layer
1	#9130	moduleManager getter across build boundary
2	#9131	shared profile UI infra
3	#9132	extract Section components from profile pages
4	#9133	composed shell + providers infra
5	#9134	composed UserProfile
6	#9135	composed OrganizationProfile
7	#9136 👈	expose @clerk/ui/experimental (public API)

Review and merge bottom-up (#9130 → #9136).

[changeset-bot]

🦋 Changeset detected

Latest commit: d61f967

The changes in this PR will be included in the next version bump.

This PR includes changesets to release 3 packages

Name	Type
@clerk/ui	Minor
@clerk/chrome-extension	Patch
@clerk/swingset	Patch

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Project	Deployment	Actions	Updated (UTC)
clerk-js-sandbox	Ready	Preview, Comment	Jul 10, 2026 8:59pm
swingset	Ready	Preview, Comment	Jul 10, 2026 8:59pm

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