fix(oauth): narrow context.lock scope in async_auth_flow (rebase of #2660 by @peisuke, closes #2847) #2661

Job	Run time
checks / pre-commit	36s
checks / readme-snippets	14s
checks / test (3.10, lowest-direct, ubuntu-latest)	55s
checks / test (3.10, lowest-direct, windows-latest)	1m 20s
checks / test (3.11, lowest-direct, ubuntu-latest)	55s
checks / test (3.11, lowest-direct, windows-latest)	1m 22s
checks / test (3.11, locked, windows-latest)	1m 29s
checks / test (3.10, locked, windows-latest)	1m 37s
checks / test (3.11, locked, ubuntu-latest)	49s
checks / test (3.10, locked, ubuntu-latest)	56s
checks / test (3.12, lowest-direct, ubuntu-latest)	1m 1s
checks / test (3.14, lowest-direct, windows-latest)	1m 17s
checks / test (3.12, locked, ubuntu-latest)	46s
checks / test (3.13, lowest-direct, windows-latest)	1m 16s
checks / test (3.14, lowest-direct, ubuntu-latest)	46s
checks / test (3.12, locked, windows-latest)	1m 30s
checks / test (3.12, lowest-direct, windows-latest)	1m 34s
checks / test (3.13, locked, ubuntu-latest)	46s
checks / test (3.13, lowest-direct, ubuntu-latest)	48s
checks / test (3.14, locked, ubuntu-latest)	2m 0s
checks / test (3.13, locked, windows-latest)	1m 24s
checks / test (3.14, locked, windows-latest)	2m 3s
all-green	2s
	25m 26s

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