fix: refresh auth context for stateful HTTP requests #1178

Job	Run time
checks / pre-commit	32s
checks / readme-snippets	12s
checks / test (3.13, locked, windows-latest)	2m 27s
checks / test (3.10, locked, windows-latest)	2m 16s
checks / test (3.12, lowest-direct, ubuntu-latest)	1m 2s
checks / test (3.13, locked, ubuntu-latest)	50s
checks / test (3.10, lowest-direct, windows-latest)	2m 17s
checks / test (3.14, lowest-direct, windows-latest)	2m 27s
checks / test (3.11, locked, windows-latest)	3m 6s
checks / test (3.10, lowest-direct, ubuntu-latest)	54s
checks / test (3.10, locked, ubuntu-latest)	53s
checks / test (3.12, lowest-direct, windows-latest)	4m 9s
checks / test (3.11, lowest-direct, windows-latest)	2m 43s
checks / test (3.12, locked, windows-latest)	3m 8s
checks / test (3.12, locked, ubuntu-latest)	55s
checks / test (3.11, locked, ubuntu-latest)	52s
checks / test (3.13, lowest-direct, ubuntu-latest)	59s
checks / test (3.11, lowest-direct, ubuntu-latest)	53s
checks / test (3.14, locked, ubuntu-latest)	2m 19s
checks / test (3.13, lowest-direct, windows-latest)	2m 46s
checks / test (3.14, lowest-direct, ubuntu-latest)	1m 17s
checks / test (3.14, locked, windows-latest)	3m 7s
all-green	4s
	40m 8s

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