refactor: flatten the methods in `Client` #223

Job	Run time
checks / readme-snippets	13s
checks / pre-commit	36s
checks / test (3.10, locked, ubuntu-latest)	44s
checks / test (3.12, lowest-direct, ubuntu-latest)	48s
checks / test (3.11, lowest-direct, ubuntu-latest)	47s
checks / test (3.11, lowest-direct, windows-latest)	2m 27s
checks / test (3.10, lowest-direct, windows-latest)	2m 15s
checks / test (3.10, lowest-direct, ubuntu-latest)	51s
checks / test (3.12, locked, ubuntu-latest)	52s
checks / test (3.11, locked, ubuntu-latest)	48s
checks / test (3.12, locked, windows-latest)	3m 49s
checks / test (3.13, locked, windows-latest)	2m 23s
checks / test (3.13, locked, ubuntu-latest)	41s
checks / test (3.14, locked, ubuntu-latest)	2m 18s
checks / test (3.13, lowest-direct, windows-latest)	2m 19s
checks / test (3.14, locked, windows-latest)	3m 9s
checks / test (3.11, locked, windows-latest)	2m 29s
checks / test (3.12, lowest-direct, windows-latest)	3m 22s
checks / test (3.14, lowest-direct, ubuntu-latest)	1m 14s
checks / test (3.10, locked, windows-latest)	2m 17s
checks / test (3.14, lowest-direct, windows-latest)	2m 23s
checks / test (3.13, lowest-direct, ubuntu-latest)	47s
all-green	2s
	37m 34s

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