Rebuild the streamable HTTP server transport around per-request dispatch #3694

Job	Run time
checks / docs	49s
checks / pre-commit	51s
checks / readme-snippets	15s
checks / test (3.11, locked, windows-latest)	1m 54s
checks / test (3.12, lowest-direct, ubuntu-latest)	1m 25s
checks / test (3.10, locked, ubuntu-latest)	1m 32s
checks / test (3.11, lowest-direct, ubuntu-latest)	1m 18s
checks / test (3.14, lowest-direct, windows-latest)	1m 51s
checks / test (3.11, locked, ubuntu-latest)	1m 27s
checks / test (3.12, locked, windows-latest)	1m 50s
checks / test (3.12, locked, ubuntu-latest)	1m 40s
checks / test (3.12, lowest-direct, windows-latest)	2m 15s
checks / test (3.10, lowest-direct, ubuntu-latest)	1m 22s
checks / test (3.10, lowest-direct, windows-latest)	1m 51s
checks / test (3.13, lowest-direct, ubuntu-latest)	1m 23s
checks / test (3.14, locked, windows-latest)	1m 51s
checks / test (3.13, locked, ubuntu-latest)	1m 11s
checks / test (3.14, lowest-direct, ubuntu-latest)	1m 9s
checks / test (3.14, locked, ubuntu-latest)	1m 25s
checks / test (3.13, locked, windows-latest)	1m 47s
checks / test (3.10, locked, windows-latest)	1m 52s
checks / test (3.13, lowest-direct, windows-latest)	1m 55s
checks / test (3.11, lowest-direct, windows-latest)	2m 16s
all-green	2s
	35m 11s

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