client-api: Rewrite websocket loop #11045

Job	Run time
Smoketests (spacetimedb-runner)	11m 37s
Test Suite	15m 33s
SDK Tests	55s
Smoketests (windows-latest)	25m 24s
Check that packages are publishable	14s
Lints	3m 14s
Test spacetimedb-update flow (x86_64-pc-windows-msvc, windows-latest)	3m 36s
Build and test wasm bindings	7m 5s
Test spacetimedb-update flow (x86_64-unknown-linux-gnu, spacetimedb-runner)	1m 0s
Test spacetimedb-update flow (aarch64-unknown-linux-gnu, arm-runner)	49s
Test spacetimedb-update flow (aarch64-apple-darwin, macos-latest)	1m 58s
	1h 11m 25s

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