feat: port legacy client integration tests #242

Job	Run time
Check Style	13s
features	38s
Test with Miri	46s
Test stable on ubuntu-latest	33s
Check MSRV (1.63)	53s
Test stable on windows-latest	1m 43s
Test stable on macOS-latest	1m 0s
Test beta on ubuntu-latest	31s
Test beta on windows-latest	1m 8s
Test beta on macOS-latest	1m 2s
Test nightly on ubuntu-latest	32s
Test nightly on windows-latest	1m 12s
Test nightly on macOS-latest	56s
Build docs	20s
CI is green	1s
	11m 28s

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