feat: add `ClientRequestContext` type alias for client-side handlers #458

Job	Run time
checks / readme-snippets	15s
checks / pre-commit	30s
checks / test (3.10, lowest-direct, ubuntu-latest)	56s
checks / test (3.10, locked, ubuntu-latest)	51s
checks / test (3.11, locked, ubuntu-latest)	48s
checks / test (3.12, locked, ubuntu-latest)	53s
checks / test (3.10, lowest-direct, windows-latest)	2m 37s
checks / test (3.11, lowest-direct, windows-latest)	2m 48s
checks / test (3.10, locked, windows-latest)	2m 33s
checks / test (3.11, lowest-direct, ubuntu-latest)	53s
checks / test (3.14, lowest-direct, ubuntu-latest)	1m 20s
checks / test (3.14, locked, windows-latest)	3m 41s
checks / test (3.14, lowest-direct, windows-latest)	2m 38s
checks / test (3.13, lowest-direct, ubuntu-latest)	56s
checks / test (3.13, locked, ubuntu-latest)	44s
checks / test (3.12, lowest-direct, ubuntu-latest)	56s
checks / test (3.12, lowest-direct, windows-latest)	3m 42s
checks / test (3.13, locked, windows-latest)	2m 23s
checks / test (3.14, locked, ubuntu-latest)	2m 22s
checks / test (3.12, locked, windows-latest)	3m 24s
checks / test (3.13, lowest-direct, windows-latest)	2m 37s
checks / test (3.11, locked, windows-latest)	2m 26s
all-green	2s
	40m 15s

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