[v2] Server registry + per-connection state; ServerRunner consumes Server[L] directly #2076

Job	Run time
checks / readme-snippets	12s
checks / pre-commit	40s
checks / test (3.11, locked, ubuntu-latest)	50s
checks / test (3.11, lowest-direct, windows-latest)	2m 41s
checks / test (3.12, locked, ubuntu-latest)	1m 1s
checks / test (3.12, lowest-direct, ubuntu-latest)	1m 4s
checks / test (3.10, lowest-direct, windows-latest)	2m 29s
checks / test (3.11, lowest-direct, ubuntu-latest)	59s
checks / test (3.14, lowest-direct, windows-latest)	2m 16s
checks / test (3.14, locked, windows-latest)	3m 26s
checks / test (3.13, locked, ubuntu-latest)	49s
checks / test (3.14, locked, ubuntu-latest)	2m 20s
checks / test (3.10, lowest-direct, ubuntu-latest)	55s
checks / test (3.10, locked, ubuntu-latest)	58s
checks / test (3.13, lowest-direct, ubuntu-latest)	57s
checks / test (3.14, lowest-direct, ubuntu-latest)	1m 22s
checks / test (3.10, locked, windows-latest)	2m 20s
checks / test (3.13, lowest-direct, windows-latest)	2m 48s
checks / test (3.12, locked, windows-latest)	3m 29s
checks / test (3.13, locked, windows-latest)	2m 21s
checks / test (3.11, locked, windows-latest)	2m 24s
checks / test (3.12, lowest-direct, windows-latest)	3m 22s
all-green	5s
	39m 48s

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