Fix thread safety of multiple `Server` instances in the same process #1205

Job	Run time
lint_and_docs (ubuntu-22.04, 3.9, 20.x)	9m 2s
build_js (ubuntu-22.04, 3.9, 20.x)	24m 11s
build_python (ubuntu-22.04, x86_64, 3.9, 20.x, false)	19m 26s
build_emscripten_wheel (ubuntu-22.04, x86_64, 3.9, 20.x)	17m 34s
build_and_test_rust (ubuntu-22.04, x86_64, 20.x, false)	10m 17s
test_emscripten_wheel (ubuntu-22.04, x86_64, 3.9, 20.x)	3m 6s
test_python (ubuntu-22.04, x86_64, 3.9, 20.x, false)	1m 24s
build_and_test_jupyterlab (ubuntu-22.04, x86_64, 3.9, 20.x, false)	1m 32s
test_js (ubuntu-22.04, 3.9, 20.x)	5m 26s
benchmark_python	0s
benchmark_js	0s
test_python_sdist	0s
publish	0s
	1h 31m 58s

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