refactor: refactor weak session implementation #10308

Job	Run time
Lints and doc tests on ubuntu-latest	9m 47s
Lints and doc tests on windows-latest	15m 35s
markdown_lint	4s
Lints and doc tests on macos-13	15m 53s
Unit tests on ubuntu-latest	25m 25s
Lints and doc tests on macos-14	8m 41s
Unit tests on windows-latest	34m 32s
Typos Check	3s
Unit tests on macos-13	43m 23s
Unit tests on macos-14	12m 44s
Memory leak checks	2m 6s
CI status checks	1s
	2h 48m 14s

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