This functionality makes me nervous honestly, because if the app allowed connections like this silently and downloads your details then wouldn't it be possible to just bypass the QR code for WhatsApp's server team?
(Also, when I point this out I always get downvotes, so, maybe a response this time?)
Unless you think FB is intentionally poisioning their web interface and serving malicious clients that break their own security you've got nothing to worry about with respect to these features.
Being able to know that the phone my chat is proxying through is about to die is pretty valuable.
Anyway, as much as I dislike Telegram, their desktop client is UX-wise miles ahead of web clients or electron trash.
The problem I have with telegram is that /by default/ it's security is very poor. It's stored and relayed by their servers so you can have a unified chat history.
However, if you hit the secret chat button I don't see a reason to think that this is stored in any way by them (and auditing the client I use confirms this for Qt linux desktop/iOS)