Add a client extension API #3248

Job	Run time
checks / pre-commit	18s
checks / docs	45s
checks / readme-snippets	11s
checks / test (3.10, locked, windows-latest)	1m 52s
checks / test (3.12, locked, windows-latest)	1m 47s
checks / test (3.11, lowest-direct, windows-latest)	2m 1s
checks / test (3.11, lowest-direct, ubuntu-latest)	1m 12s
checks / test (3.10, locked, ubuntu-latest)	1m 23s
checks / test (3.11, locked, ubuntu-latest)	1m 15s
checks / test (3.10, lowest-direct, windows-latest)	2m 2s
checks / test (3.10, lowest-direct, ubuntu-latest)	1m 13s
checks / test (3.14, locked, windows-latest)	2m 29s
checks / test (3.13, locked, ubuntu-latest)	1m 11s
checks / test (3.14, lowest-direct, ubuntu-latest)	1m 12s
checks / test (3.12, lowest-direct, windows-latest)	1m 54s
checks / test (3.13, lowest-direct, windows-latest)	2m 18s
checks / test (3.13, lowest-direct, ubuntu-latest)	1m 19s
checks / test (3.12, lowest-direct, ubuntu-latest)	1m 22s
checks / test (3.13, locked, windows-latest)	2m 2s
checks / test (3.12, locked, ubuntu-latest)	1m 29s
checks / test (3.11, locked, windows-latest)	2m 6s
checks / test (3.14, locked, ubuntu-latest)	2m 7s
checks / test (3.14, lowest-direct, windows-latest)	1m 52s
all-green	3s
	35m 23s

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