fix(client): forward User-Agent through OAuth auth flow #2036

Job	Run time
checks / readme-snippets	15s
checks / pre-commit	39s
checks / test (3.11, locked, ubuntu-latest)	55s
checks / test (3.12, lowest-direct, windows-latest)	3m 49s
checks / test (3.10, lowest-direct, ubuntu-latest)	57s
checks / test (3.11, locked, windows-latest)	2m 33s
checks / test (3.12, locked, ubuntu-latest)	58s
checks / test (3.11, lowest-direct, windows-latest)	2m 27s
checks / test (3.10, lowest-direct, windows-latest)	2m 22s
checks / test (3.12, lowest-direct, ubuntu-latest)	1m 0s
checks / test (3.12, locked, windows-latest)	3m 38s
checks / test (3.13, locked, windows-latest)	3m 14s
checks / test (3.10, locked, ubuntu-latest)	49s
checks / test (3.11, lowest-direct, ubuntu-latest)	59s
checks / test (3.10, locked, windows-latest)	2m 22s
checks / test (3.14, lowest-direct, ubuntu-latest)	1m 20s
checks / test (3.13, locked, ubuntu-latest)	47s
checks / test (3.14, lowest-direct, windows-latest)	2m 18s
checks / test (3.13, lowest-direct, windows-latest)	2m 45s
checks / test (3.14, locked, ubuntu-latest)	2m 23s
checks / test (3.13, lowest-direct, ubuntu-latest)	1m 1s
checks / test (3.14, locked, windows-latest)	3m 53s
all-green	5s
	41m 29s

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