refactor: flatten the methods in `Client` #222

Job	Run time
checks / readme-snippets	11s
checks / pre-commit	18s
checks / test (3.11, locked, ubuntu-latest)	47s
checks / test (3.11, lowest-direct, ubuntu-latest)	43s
checks / test (3.10, lowest-direct, ubuntu-latest)	47s
checks / test (3.12, locked, windows-latest)	3m 46s
checks / test (3.10, locked, ubuntu-latest)	44s
checks / test (3.12, lowest-direct, windows-latest)	3m 31s
checks / test (3.10, locked, windows-latest)	2m 17s
checks / test (3.11, lowest-direct, windows-latest)	2m 48s
checks / test (3.10, lowest-direct, windows-latest)	2m 12s
checks / test (3.12, locked, ubuntu-latest)	51s
checks / test (3.13, lowest-direct, windows-latest)	2m 20s
checks / test (3.14, locked, ubuntu-latest)	2m 26s
checks / test (3.12, lowest-direct, ubuntu-latest)	47s
checks / test (3.13, locked, windows-latest)	2m 24s
checks / test (3.14, lowest-direct, windows-latest)	2m 10s
checks / test (3.13, locked, ubuntu-latest)	45s
checks / test (3.11, locked, windows-latest)	2m 29s
checks / test (3.14, lowest-direct, ubuntu-latest)	1m 17s
checks / test (3.14, locked, windows-latest)	3m 12s
checks / test (3.13, lowest-direct, ubuntu-latest)	45s
all-green	5s
	37m 35s

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