fix(oauth): narrow context.lock scope in async_auth_flow (rebase of #2660 by @peisuke, closes #2847) #2931

Job	Run time
checks / readme-snippets	10s
checks / pre-commit	43s
checks / test (3.11, lowest-direct, windows-latest)	1m 32s
checks / test (3.10, lowest-direct, ubuntu-latest)	1m 5s
checks / test (3.10, lowest-direct, windows-latest)	1m 21s
checks / test (3.11, lowest-direct, ubuntu-latest)	59s
checks / test (3.14, lowest-direct, windows-latest)	1m 23s
checks / test (3.12, locked, ubuntu-latest)	1m 7s
checks / test (3.14, locked, ubuntu-latest)	2m 2s
checks / test (3.10, locked, windows-latest)	1m 6s
checks / test (3.12, lowest-direct, ubuntu-latest)	1m 8s
checks / test (3.11, locked, ubuntu-latest)	1m 0s
checks / test (3.10, locked, ubuntu-latest)	1m 5s
checks / test (3.11, locked, windows-latest)	1m 35s
checks / test (3.14, lowest-direct, ubuntu-latest)	55s
checks / test (3.12, lowest-direct, windows-latest)	1m 31s
checks / test (3.12, locked, windows-latest)	1m 55s
checks / test (3.13, lowest-direct, windows-latest)	1m 43s
checks / test (3.13, locked, ubuntu-latest)	56s
checks / test (3.14, locked, windows-latest)	4m 37s
checks / test (3.13, lowest-direct, ubuntu-latest)	1m 6s
checks / test (3.13, locked, windows-latest)	1m 26s
all-green	5s
	30m 30s

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