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feat(website): bring the live demo into the homepage hero #2642

Job	Run time
Typecheck (tests)	47s
AppStream metadata	15s
Rust check (Windows compositor)	3m 35s
Swift test (macOS capture helper)	1m 20s
Type Check	42s
Test	2m 7s
Rust test (macOS compositor)	3m 55s
Lint	32s
Rust test (Linux compositor)	4m 12s
Docs	8s
Validate PR title (semantic)	4s
Build	59s
	18m 36s