Drop sooner mutex guards during open/accept #10097

Job	Run time
Unit tests on ubuntu-latest	2m 51s
Unit tests on windows-latest	6m 53s
Typos Check	3s
Unit tests on macos-13	4m 28s
Lints and doc tests on ubuntu-latest	12m 16s
Unit tests on macos-14	3m 3s
Lints and doc tests on windows-latest	17m 5s
markdown_lint	8s
Lints and doc tests on macos-13	24m 59s
Lints and doc tests on macos-14	8m 29s
Memory leak checks	2m 25s
CI status checks	1s
	1h 22m 41s

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