[v9]: Remove `dart:html` usage in favour of `package:web` #1787

Job	Run time
cancel-previous-workflow	4s
macos \| stable	1m 27s
macos \| beta	1m 9s
linux \| stable	1m 39s
linux \| beta	1m 48s
windows \| stable	2m 55s
windows \| beta	4m 14s
analyze / cancel-previous-workflow	2s
analyze / analyze	1m 24s
analyze / package-analysis	1m 38s
	16m 20s

Provide feedback