fix(oauth): narrow context.lock scope in async_auth_flow (rebase of #2660 by @peisuke, closes #2847) #2895

Job	Run time
checks / pre-commit	46s
checks / readme-snippets	11s
checks / test (3.11, locked, ubuntu-latest)	57s
checks / test (3.11, lowest-direct, ubuntu-latest)	1m 1s
checks / test (3.13, lowest-direct, ubuntu-latest)	1m 0s
checks / test (3.14, lowest-direct, ubuntu-latest)	59s
checks / test (3.14, lowest-direct, windows-latest)	2m 0s
checks / test (3.13, locked, windows-latest)	1m 24s
checks / test (3.12, locked, ubuntu-latest)	1m 7s
checks / test (3.10, locked, windows-latest)	1m 31s
checks / test (3.13, locked, ubuntu-latest)	51s
checks / test (3.13, lowest-direct, windows-latest)	1m 33s
checks / test (3.10, lowest-direct, windows-latest)	1m 40s
checks / test (3.12, locked, windows-latest)	1m 33s
checks / test (3.14, locked, ubuntu-latest)	1m 57s
checks / test (3.12, lowest-direct, windows-latest)	1m 39s
checks / test (3.14, locked, windows-latest)	2m 15s
checks / test (3.11, lowest-direct, windows-latest)	1m 36s
checks / test (3.10, locked, ubuntu-latest)	10s
checks / test (3.11, locked, windows-latest)	1m 17s
checks / test (3.12, lowest-direct, ubuntu-latest)	1m 7s
checks / test (3.10, lowest-direct, ubuntu-latest)	59s
all-green	5s
	27m 38s

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