Fix stale auth context in stateful StreamableHTTP sessions #1692

Job	Run time
checks / pre-commit	39s
checks / readme-snippets	11s
checks / test (3.10, lowest-direct, windows-latest)	2m 37s
checks / test (3.10, locked, ubuntu-latest)	48s
checks / test (3.10, locked, windows-latest)	2m 19s
checks / test (3.11, lowest-direct, ubuntu-latest)	49s
checks / test (3.12, lowest-direct, ubuntu-latest)	55s
checks / test (3.12, locked, ubuntu-latest)	56s
checks / test (3.11, locked, ubuntu-latest)	40s
checks / test (3.13, lowest-direct, windows-latest)	2m 31s
checks / test (3.11, locked, windows-latest)	2m 13s
checks / test (3.14, lowest-direct, ubuntu-latest)	1m 9s
checks / test (3.14, lowest-direct, windows-latest)	2m 9s
checks / test (3.14, locked, windows-latest)	2m 58s
checks / test (3.11, lowest-direct, windows-latest)	2m 41s
checks / test (3.13, lowest-direct, ubuntu-latest)	52s
checks / test (3.13, locked, windows-latest)	2m 1s
checks / test (3.12, locked, windows-latest)	3m 10s
checks / test (3.13, locked, ubuntu-latest)	49s
checks / test (3.14, locked, ubuntu-latest)	2m 13s
checks / test (3.10, lowest-direct, ubuntu-latest)	57s
checks / test (3.12, lowest-direct, windows-latest)	3m 23s
all-green	4s
	37m 4s

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