feat: add `ClientRequestContext` type alias for client-side handlers #457

Job	Run time
checks / readme-snippets	11s
checks / pre-commit	37s
checks / test (3.12, locked, windows-latest)	3m 34s
checks / test (3.14, lowest-direct, ubuntu-latest)	1m 15s
checks / test (3.10, lowest-direct, ubuntu-latest)	58s
checks / test (3.11, lowest-direct, ubuntu-latest)	52s
checks / test (3.13, lowest-direct, windows-latest)	2m 44s
checks / test (3.10, locked, ubuntu-latest)	50s
checks / test (3.12, locked, ubuntu-latest)	57s
checks / test (3.14, lowest-direct, windows-latest)	2m 23s
checks / test (3.11, lowest-direct, windows-latest)	2m 45s
checks / test (3.14, locked, windows-latest)	3m 26s
checks / test (3.13, locked, windows-latest)	2m 28s
checks / test (3.13, lowest-direct, ubuntu-latest)	49s
checks / test (3.12, lowest-direct, windows-latest)	3m 49s
checks / test (3.11, locked, windows-latest)	2m 35s
checks / test (3.13, locked, ubuntu-latest)	48s
checks / test (3.10, locked, windows-latest)	2m 26s
checks / test (3.11, locked, ubuntu-latest)	51s
checks / test (3.14, locked, ubuntu-latest)	2m 12s
checks / test (3.12, lowest-direct, ubuntu-latest)	1m 1s
checks / test (3.10, lowest-direct, windows-latest)	2m 33s
all-green	4s
	40m 8s

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