Rebuild the streamable HTTP server transport around per-request dispatch #3697

Job	Run time
checks / docs	1m 4s
checks / pre-commit	57s
checks / test (3.10, locked, ubuntu-latest)	1m 32s
checks / test (3.11, lowest-direct, windows-latest)	1m 52s
checks / test (3.13, locked, windows-latest)	1m 43s
checks / test (3.11, locked, windows-latest)	1m 58s
checks / test (3.13, locked, ubuntu-latest)	1m 10s
checks / test (3.12, lowest-direct, ubuntu-latest)	1m 26s
checks / readme-snippets	16s
checks / test (3.13, lowest-direct, windows-latest)	1m 55s
checks / test (3.14, locked, windows-latest)	2m 26s
checks / test (3.12, lowest-direct, windows-latest)	1m 50s
checks / test (3.11, lowest-direct, ubuntu-latest)	1m 24s
checks / test (3.10, locked, windows-latest)	1m 48s
checks / test (3.13, lowest-direct, ubuntu-latest)	1m 23s
checks / test (3.12, locked, windows-latest)	1m 56s
checks / test (3.12, locked, ubuntu-latest)	1m 35s
checks / test (3.10, lowest-direct, ubuntu-latest)	1m 34s
checks / test (3.14, lowest-direct, ubuntu-latest)	1m 16s
checks / test (3.14, lowest-direct, windows-latest)	2m 12s
checks / test (3.10, lowest-direct, windows-latest)	1m 51s
checks / test (3.11, locked, ubuntu-latest)	1m 17s
checks / test (3.14, locked, ubuntu-latest)	1m 20s
all-green	5s
	35m 50s

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