fix(oauth): narrow context.lock scope in async_auth_flow (rebase of #2660 by @peisuke, closes #2847) #2655

Job	Run time
checks / readme-snippets	14s
checks / pre-commit	34s
checks / test (3.10, locked, windows-latest)	1m 26s
checks / test (3.11, lowest-direct, ubuntu-latest)	40s
checks / test (3.12, lowest-direct, ubuntu-latest)	46s
checks / test (3.10, lowest-direct, ubuntu-latest)	43s
checks / test (3.12, locked, windows-latest)	1m 11s
checks / test (3.12, lowest-direct, windows-latest)	1m 29s
checks / test (3.14, lowest-direct, ubuntu-latest)	38s
checks / test (3.13, lowest-direct, windows-latest)	1m 26s
checks / test (3.10, lowest-direct, windows-latest)	1m 8s
checks / test (3.11, locked, ubuntu-latest)	41s
checks / test (3.13, lowest-direct, ubuntu-latest)	40s
checks / test (3.11, locked, windows-latest)	1m 27s
checks / test (3.14, lowest-direct, windows-latest)	1m 7s
checks / test (3.13, locked, ubuntu-latest)	40s
checks / test (3.10, locked, ubuntu-latest)	44s
checks / test (3.12, locked, ubuntu-latest)	42s
checks / test (3.11, lowest-direct, windows-latest)	1m 22s
checks / test (3.14, locked, windows-latest)	2m 31s
checks / test (3.13, locked, windows-latest)	1m 29s
checks / test (3.14, locked, ubuntu-latest)	1m 51s
all-green	2s
	23m 31s

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