Rebuild the streamable HTTP server transport around per-request dispatch #3723

Job	Run time
checks / pre-commit	46s
checks / docs	52s
checks / test (3.11, lowest-direct, windows-latest)	2m 21s
checks / test (3.13, lowest-direct, ubuntu-latest)	1m 14s
checks / test (3.13, locked, windows-latest)	1m 58s
checks / test (3.10, lowest-direct, ubuntu-latest)	1m 30s
checks / test (3.14, locked, ubuntu-latest)	1m 22s
checks / test (3.12, locked, windows-latest)	2m 7s
checks / readme-snippets	11s
checks / test (3.13, lowest-direct, windows-latest)	2m 9s
checks / test (3.12, lowest-direct, ubuntu-latest)	1m 21s
checks / test (3.14, locked, windows-latest)	1m 59s
checks / test (3.12, lowest-direct, windows-latest)	2m 11s
checks / test (3.14, lowest-direct, ubuntu-latest)	1m 24s
checks / test (3.11, locked, ubuntu-latest)	1m 21s
checks / test (3.14, lowest-direct, windows-latest)	1m 51s
checks / test (3.13, locked, ubuntu-latest)	1m 16s
checks / test (3.11, lowest-direct, ubuntu-latest)	1m 0s
checks / test (3.12, locked, ubuntu-latest)	1m 37s
checks / test (3.10, locked, windows-latest)	2m 2s
checks / test (3.10, locked, ubuntu-latest)	1m 12s
checks / test (3.11, locked, windows-latest)	1m 57s
checks / test (3.10, lowest-direct, windows-latest)	1m 50s
all-green	5s
	35m 36s

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