Migrate from `dart:html` to `package:web` #2134

Job	Run time
dartanalyze	59s
clippy (linux)	2m 59s
dartfmt	48s
clippy (macos)	2m 34s
ktfmt	8s
clippy (windows)	6m 33s
rustfmt	14s
build (macos)	1m 17s
build (linux)	5m 11s
build (windows)	9m 47s
rustdoc (linux)	3m 7s
swiftformat	9s
rustdoc (macos)	4m 11s
rustdoc (windows)	6m 58s
test (example, ${{ matrix.platform }})	0s
pr	0s
dart pub publish (pub.dev)	0s
release (GitHub)	0s
	44m 55s

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