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feat(website): bring the live demo into the homepage hero #2632

Job	Run time
Typecheck (tests)	48s
Lint	31s
Docs	10s
Validate PR title (semantic)	5s
Build	1m 2s
AppStream metadata	13s
Rust test (Linux compositor)	6m 27s
Type Check	44s
Swift test (macOS capture helper)	1m 17s
Rust test (macOS compositor)	4m 27s
Test	2m 52s
Rust check (Windows compositor)	3m 12s
	21m 48s