refactor: connect-first stream lifecycle for sse and streamable_http #1476

Job	Run time
checks / readme-snippets	14s
checks / pre-commit	35s
checks / test (3.11, locked, windows-latest)	2m 19s
checks / test (3.13, lowest-direct, windows-latest)	3m 25s
checks / test (3.10, lowest-direct, ubuntu-latest)	57s
checks / test (3.12, locked, ubuntu-latest)	1m 1s
checks / test (3.14, lowest-direct, ubuntu-latest)	1m 15s
checks / test (3.10, locked, windows-latest)	2m 22s
checks / test (3.12, lowest-direct, windows-latest)	3m 56s
checks / test (3.13, locked, windows-latest)	2m 29s
checks / test (3.13, lowest-direct, ubuntu-latest)	55s
checks / test (3.12, locked, windows-latest)	3m 32s
checks / test (3.10, locked, ubuntu-latest)	51s
checks / test (3.11, lowest-direct, ubuntu-latest)	55s
checks / test (3.14, lowest-direct, windows-latest)	2m 36s
checks / test (3.10, lowest-direct, windows-latest)	2m 42s
checks / test (3.11, locked, ubuntu-latest)	51s
checks / test (3.12, lowest-direct, ubuntu-latest)	59s
checks / test (3.13, locked, ubuntu-latest)	49s
checks / test (3.11, lowest-direct, windows-latest)	3m 8s
checks / test (3.14, locked, ubuntu-latest)	2m 22s
checks / test (3.14, locked, windows-latest)	3m 14s
all-green	4s
	41m 31s

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