refactor: connect-first stream lifecycle for sse and streamable_http … #1486

Job	Run time
checks / readme-snippets	14s
checks / pre-commit	38s
checks / test (3.10, lowest-direct, ubuntu-latest)	1m 1s
checks / test (3.10, locked, ubuntu-latest)	52s
checks / test (3.11, lowest-direct, ubuntu-latest)	54s
checks / test (3.10, lowest-direct, windows-latest)	2m 58s
checks / test (3.10, locked, windows-latest)	3m 1s
checks / test (3.11, lowest-direct, windows-latest)	2m 49s
checks / test (3.13, locked, ubuntu-latest)	50s
checks / test (3.12, locked, ubuntu-latest)	55s
checks / test (3.13, lowest-direct, windows-latest)	2m 50s
checks / test (3.11, locked, windows-latest)	2m 37s
checks / test (3.11, locked, ubuntu-latest)	55s
checks / test (3.14, lowest-direct, ubuntu-latest)	1m 17s
checks / test (3.13, lowest-direct, ubuntu-latest)	54s
checks / test (3.14, locked, ubuntu-latest)	2m 20s
checks / test (3.14, locked, windows-latest)	3m 18s
checks / test (3.12, lowest-direct, ubuntu-latest)	1m 5s
checks / test (3.12, locked, windows-latest)	3m 27s
checks / test (3.14, lowest-direct, windows-latest)	2m 32s
checks / test (3.12, lowest-direct, windows-latest)	4m 17s
checks / test (3.13, locked, windows-latest)	2m 38s
all-green	3s
	42m 25s

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