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. Merges the full composed UserProfile / OrganizationProfile API.

Changesets live only on the release PR #9144; this PR carries none.

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Stack

Reviewed as a stack. The 7 PRs merge bottom-up into release branch #9144, which integrates into main as a single unit.

#	PR	Layer
–	#9144	release → main (integration)
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)

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Latest commit: 84be728

Merging this PR will not cause a version bump for any packages. If these changes should not result in a new version, you're good to go. If these changes should result in a version bump, you need to add a changeset.

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Project	Deployment	Actions	Updated (UTC)
clerk-js-sandbox	Ready	Preview, Comment	Jul 13, 2026 7:21pm
swingset	Error		Jul 13, 2026 7:21pm

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