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> Even assuming a lack of malicious intent, what's stopping NSA from hacking into Signal's infrastructure and logging who's talking to who along with timestamps?

Sealed Sender, the second link in the comment you've replied to. The indicator is off by default, but you can enable it under Settings → Privacy → Advanced. If I remember correctly, it doesn't work for the very first message you exchange with someone, but then it turns on and remains on.

In layman terms, it turns "from A; to B; content: <encrypted>" into "to B; content: <encrypted>". Their infrastructure doesn't need to know the "from" part to serve its purpose, so they strip it away.

If it was the other way around, they'd have to give that info to the (US) court. Same as any other US-based business, it's not optional, they can't ignore such requests, they can't lie, otherwise they'd be placing themselves in legal troubles for a random nobody that happens to be using their product. So, when I see this page, I fully believe them: https://signal.org/bigbrother/. If I didn't, my first step would be to look up those court cases from alternate sources.