fix(auth): get_access_token reflects current request in stateful sessions #3250

Job	Run time
checks / readme-snippets	16s
checks / docs	43s
checks / pre-commit	47s
checks / test (3.10, lowest-direct, ubuntu-latest)	1m 16s
checks / test (3.11, lowest-direct, windows-latest)	1m 53s
checks / test (3.12, lowest-direct, ubuntu-latest)	1m 19s
checks / test (3.14, locked, windows-latest)	2m 56s
checks / test (3.10, locked, ubuntu-latest)	1m 25s
checks / test (3.12, locked, ubuntu-latest)	1m 38s
checks / test (3.14, lowest-direct, windows-latest)	1m 50s
checks / test (3.12, lowest-direct, windows-latest)	1m 55s
checks / test (3.13, lowest-direct, ubuntu-latest)	1m 13s
checks / test (3.13, lowest-direct, windows-latest)	1m 56s
checks / test (3.14, locked, ubuntu-latest)	2m 15s
checks / test (3.10, lowest-direct, windows-latest)	2m 1s
checks / test (3.13, locked, windows-latest)	1m 47s
checks / test (3.11, locked, windows-latest)	1m 56s
checks / test (3.11, locked, ubuntu-latest)	1m 10s
checks / test (3.10, locked, windows-latest)	1m 50s
checks / test (3.11, lowest-direct, ubuntu-latest)	1m 12s
checks / test (3.12, locked, windows-latest)	1m 54s
checks / test (3.13, locked, ubuntu-latest)	1m 15s
checks / test (3.14, lowest-direct, ubuntu-latest)	1m 14s
all-green	5s
	35m 46s

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