refactor: connect-first stream lifecycle for sse and streamable_http #1454

Job	Run time
checks / pre-commit	40s
checks / readme-snippets	13s
checks / test (3.10, lowest-direct, windows-latest)	2m 38s
checks / test (3.10, locked, windows-latest)	2m 44s
checks / test (3.10, lowest-direct, ubuntu-latest)	52s
checks / test (3.12, locked, ubuntu-latest)	57s
checks / test (3.12, lowest-direct, windows-latest)	3m 50s
checks / test (3.14, locked, ubuntu-latest)	2m 19s
checks / test (3.13, locked, windows-latest)	3m 0s
checks / test (3.12, lowest-direct, ubuntu-latest)	57s
checks / test (3.10, locked, ubuntu-latest)	52s
checks / test (3.14, locked, windows-latest)	3m 16s
checks / test (3.14, lowest-direct, windows-latest)	2m 58s
checks / test (3.11, locked, windows-latest)	2m 39s
checks / test (3.13, lowest-direct, windows-latest)	2m 57s
checks / test (3.13, lowest-direct, ubuntu-latest)	57s
checks / test (3.11, lowest-direct, ubuntu-latest)	58s
checks / test (3.12, locked, windows-latest)	3m 29s
checks / test (3.11, lowest-direct, windows-latest)	2m 48s
checks / test (3.13, locked, ubuntu-latest)	46s
checks / test (3.11, locked, ubuntu-latest)	51s
checks / test (3.14, lowest-direct, ubuntu-latest)	1m 20s
all-green	4s
	42m 5s

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