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Signal works on desktop nicely, but you still need the mobile app on a smart phone in order for it to work.

I'm still looking for one that doesn't require a mobile phone at all. Let me know if you find one. :)

I love Discord, but you know... Discord isn't really... anything privacy at all.

Matrix and XMPP are a couple E2EE decentralized protocols that can work only on desktop and do not require a phone or phone number.