refactor: flatten the methods in `Client` #220

Job	Run time
checks / readme-snippets	10s
checks / pre-commit	30s
checks / test (3.11, lowest-direct, ubuntu-latest)	46s
checks / test (3.11, locked, ubuntu-latest)	44s
checks / test (3.11, locked, windows-latest)	2m 44s
checks / test (3.12, lowest-direct, windows-latest)	3m 34s
checks / test (3.12, locked, windows-latest)	3m 33s
checks / test (3.10, locked, windows-latest)	2m 30s
checks / test (3.13, lowest-direct, windows-latest)	2m 19s
checks / test (3.12, locked, ubuntu-latest)	53s
checks / test (3.12, lowest-direct, ubuntu-latest)	49s
checks / test (3.10, locked, ubuntu-latest)	42s
checks / test (3.11, lowest-direct, windows-latest)	2m 18s
checks / test (3.13, lowest-direct, ubuntu-latest)	43s
checks / test (3.13, locked, windows-latest)	2m 39s
checks / test (3.14, lowest-direct, ubuntu-latest)	1m 13s
checks / test (3.10, lowest-direct, ubuntu-latest)	48s
checks / test (3.10, lowest-direct, windows-latest)	2m 15s
checks / test (3.14, lowest-direct, windows-latest)	2m 9s
checks / test (3.13, locked, ubuntu-latest)	42s
checks / test (3.14, locked, windows-latest)	3m 10s
checks / test (3.14, locked, ubuntu-latest)	2m 19s
all-green	4s
	37m 34s

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