Adopt `ClientContext` changes #101

Job	Run time
Unit Tests / Construct unit test matrix	3s
Cxx Interop / Construct Cxx interop matrix	3s
Soundness / Swift license headers check	4s
Integration Tests / Linux (5.9)	24s
Integration Tests / Linux (5.10)	24s
Integration Tests / Linux (6.0)	5m 45s
Integration Tests / Windows (6.0)	1s
Integration Tests / Linux (nightly-6.0)	3m 12s
Integration Tests / Linux (nightly-main)	3m 0s
Soundness / API breakage check	3m 29s
Integration Tests / Windows (nightly-6.0)	1s
Soundness / Documentation check	2m 36s
Soundness / Unacceptable language check	2s
Integration Tests / Windows (nightly-main)	1s
Soundness / Broken symlinks check	2s
Soundness / License headers check	5s
Soundness / Format check	38s
Soundness / Python lint check	4s
Soundness / Shell check	30s
Soundness / YAML lint check	5s
Cxx Interop / Cxx interop / Linux (6.0)	2m 15s
Unit Tests / Unit tests / Linux (6.0)	3m 3s
Cxx Interop / Cxx interop / Linux (nightly-6.0)	2m 33s
Cxx Interop / Cxx interop / Linux (nightly-main)	2m 32s
Unit Tests / Unit tests / Linux (nightly-6.0)	3m 22s
Unit Tests / Unit tests / Linux (nightly-main)	3m 13s
	37m 27s

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