feat(shared,ui): Add useClerkMutation to @clerk/shared/react for query-core-backed mutations

[alexcarpenter]

Description

Checklist

• pnpm test runs as expected.
• pnpm build runs as expected.
• (If applicable) JSDoc comments have been added or updated for any package exports
• (If applicable) Documentation has been updated

Type of change

• 🐛 Bug fix
• 🌟 New feature
• 🔨 Breaking change
• 📖 Refactoring / dependency upgrade / documentation
• other:

[changeset-bot]

🦋 Changeset detected

Latest commit: b21f13b

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

This PR includes changesets to release 23 packages

Name	Type
@clerk/shared	Minor
@clerk/ui	Patch
@clerk/astro	Patch
@clerk/backend	Patch
@clerk/chrome-extension	Patch
@clerk/clerk-js	Patch
@clerk/electron	Patch
@clerk/expo-passkeys	Patch
@clerk/expo	Patch
@clerk/express	Patch
@clerk/fastify	Patch
@clerk/headless	Patch
@clerk/hono	Patch
@clerk/localizations	Patch
@clerk/msw	Patch
@clerk/nextjs	Patch
@clerk/nuxt	Patch
@clerk/react-router	Patch
@clerk/react	Patch
@clerk/tanstack-react-start	Patch
@clerk/testing	Patch
@clerk/vue	Patch
@clerk/swingset	Patch

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Project	Deployment	Actions	Updated (UTC)
clerk-js-sandbox	Ready	Preview, Comment	Jun 26, 2026 9:17pm
swingset	Ready	Preview, Comment	Jun 26, 2026 9:17pm

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@clerk/astro

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@clerk/upgrade

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@clerk/vue

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commit: b21f13b