web: Implement pasting text using Clipboard API #23398

Job	Run time
Paths filter	6s
Check dependencies	1m 30s
Test Rust stable / ubuntu-22.04	10m 17s
Test Rust ${{ matrix.rust_version }} / ${{ matrix.os }}	0s
Lints with Rust stable	4m 18s
Test Rust stable / windows-latest	17m 59s
Lints with Rust beta	3m 4s
Test Rust stable / macos-14	6m 28s
Test Rust nightly / ubuntu-22.04	6m 26s
Lints with Rust nightly	4m 25s
Test Rust beta / ubuntu-22.04	6m 32s
	1h 1m 5s

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