Add support for client context and middleware (unstable) #865

Job	Run time
👀 Integration Test / ubuntu-latest / node@22 / firefox	31m 47s
👀 Integration Test / macos-latest / node@22 / webkit	40m 54s
👀 Integration Test / windows-latest / node@22 / msedge	42m 35s
	1h 55m 16s

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