refactor: flatten the methods in `Client` #219

Job	Run time
checks / readme-snippets	13s
checks / pre-commit	31s
checks / test (3.10, locked, ubuntu-latest)	45s
checks / test (3.14, lowest-direct, ubuntu-latest)	1m 9s
checks / test (3.10, locked, windows-latest)	2m 20s
checks / test (3.10, lowest-direct, windows-latest)	2m 16s
checks / test (3.12, lowest-direct, ubuntu-latest)	45s
checks / test (3.11, locked, ubuntu-latest)	41s
checks / test (3.11, lowest-direct, ubuntu-latest)	43s
checks / test (3.13, lowest-direct, ubuntu-latest)	39s
checks / test (3.10, lowest-direct, ubuntu-latest)	41s
checks / test (3.13, locked, ubuntu-latest)	42s
checks / test (3.13, lowest-direct, windows-latest)	2m 47s
checks / test (3.14, lowest-direct, windows-latest)	2m 14s
checks / test (3.13, locked, windows-latest)	2m 51s
checks / test (3.12, locked, ubuntu-latest)	50s
checks / test (3.12, locked, windows-latest)	3m 21s
checks / test (3.11, lowest-direct, windows-latest)	2m 22s
checks / test (3.12, lowest-direct, windows-latest)	3m 17s
checks / test (3.11, locked, windows-latest)	2m 41s
checks / test (3.14, locked, ubuntu-latest)	2m 18s
checks / test (3.14, locked, windows-latest)	3m 14s
all-green	4s
	37m 24s

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