Replace Tornado with AnyIO #1951

Job	Run time
check_release	2m 6s
build (ubuntu-latest, 3.8)	2m 3s
build (ubuntu-latest, 3.11)	2m 4s
link_check	2m 4s
build (windows-latest, 3.8)	1m 56s
build (windows-latest, 3.11)	1m 56s
Make SDist	39s
test_docs	1m 57s
build (macos-latest, 3.8)	2m 1s
build (macos-latest, 3.11)	2m 3s
Test Lint	1m 3s
Test Minimum Versions	2m 5s
build (windows-latest, 3.9)	1m 57s
build (ubuntu-latest, pypy-3.8)	2m 3s
Test Prereleases	2m 2s
build (macos-latest, 3.10)	1m 59s
test_without_debugpy (ubuntu-latest, 3.9)	1m 39s
Install from SDist and Test	1m 16s
coverage	1s
tests_check	2s
	32m 56s

Provide feedback