refactor(shared,clerk-js,react): move QueryClient ownership into @clerk/shared #27632

Job	Run time
Check Permissions	5s
Formatting \| Dedupe \| Changeset	58s
Build Packages	1m 10s
Static analysis	3m 0s
Unit Tests (**)	3m 20s
Publish with pkg-pr-new	1m 32s
Unit Tests (**)	2m 5s
Integration Tests (ap-flows, chrome)	2m 14s
Integration Tests (express, chrome)	2m 6s
Integration Tests (sessions:staging, chrome)	2m 40s
Integration Tests (generic, chrome)	5m 41s
Integration Tests (localhost, chrome)	2m 27s
Integration Tests (sessions, chrome)	2m 40s
Integration Tests (fastify, chrome)	2m 19s
Integration Tests (handshake:staging, chrome)	1m 53s
Integration Tests (astro, chrome)	2m 56s
Integration Tests (vue, chrome)	2m 4s
Integration Tests (tanstack-react-start, chrome)	2m 2s
Integration Tests (nuxt, chrome)	2m 37s
Integration Tests (chrome-extension, chrome)	3m 44s
Integration Tests (react-router, chrome)	2m 9s
Integration Tests (machine, chrome)	5m 43s
Integration Tests (billing, chrome)	6m 19s
Integration Tests (nextjs, chrome, 15)	7m 46s
Integration Tests (hono, chrome)	3m 2s
Integration Tests (nextjs, chrome, 16)	5m 17s
Integration Tests (custom, chrome)	2m 37s
Integration Tests (handshake, chrome)	2m 41s
Integration Tests (quickstart, chrome, 16)	3m 19s
Integration Tests (quickstart, chrome, 15)	3m 14s
Integration Tests (cache-components, chrome, 16)	3m 51s
	1h 33m 31s

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