Adopt `ClientContext` changes #100

Job	Run time
Soundness / Swift license headers check	5s
Cxx Interop / Construct Cxx interop matrix	2s
Unit Tests / Construct unit test matrix	3s
Integration Tests / Windows (6.0)	1s
Integration Tests / Windows (nightly-6.0)	2s
Integration Tests / Linux (5.9)	23s
Integration Tests / Windows (nightly-main)	3s
Integration Tests / Linux (5.10)	24s
Soundness / API breakage check	3m 32s
Soundness / Documentation check	2m 38s
Integration Tests / Linux (6.0)	5m 40s
Integration Tests / Linux (nightly-6.0)	3m 10s
Soundness / Broken symlinks check	3s
Integration Tests / Linux (nightly-main)	3m 3s
Soundness / License headers check	5s
Soundness / Unacceptable language check	5s
Soundness / Python lint check	11s
Soundness / Format check	33s
Soundness / Shell check	32s
Soundness / YAML lint check	2s
Unit Tests / Unit tests / Linux (6.0)	3m 8s
Unit Tests / Unit tests / Linux (nightly-6.0)	3m 19s
Unit Tests / Unit tests / Linux (nightly-main)	3m 5s
Cxx Interop / Cxx interop / Linux (6.0)	2m 16s
Cxx Interop / Cxx interop / Linux (nightly-6.0)	2m 32s
Cxx Interop / Cxx interop / Linux (nightly-main)	2m 28s
	37m 25s

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