Signal does have sync, but it works exactly the same way as Whatsapp's does, requiring your phone to be on and connected
Telegram's secret chats are also client-specific and not synced, and I have no idea how it would even be possible to have e2e chats synced on multiple devices without having a "main" device that's doing the actual crypto or sharing the secret key
I got fooled by Signal's requirement of a phone for the activation and thought it was also required for normal usage, I guess that's better than Whatsapp, though being able to register and use it without a phone at all would be even better (even Telegram doesn't do this though, IIRC it requires a phone number)
You are totally wrong. The phone number aspect has absolutely nothing to do with the e2e client problem.
Its possible to have e2e on multiple clients, with or without a phone number attached to it. There are multiple chat clients that can do it, some with, some without phone number. Signal requires phone number and does it, Wire and Riot do it without a phone number.
Telegram just don't actually care about security or privacy. Unencrypted defaults, all conversation saved on the server, even if you use their 'roll your own' crypt secret chats you lose most of the functionality that actually go people to use Telegram in the first place.
Telegram essentially has no usable e2e crypto to speak off. Secret chats are a usability and security nightmare.
People should use Riot (Matrix) or Wire. Those are much better.
Telegram's secret chats are also client-specific and not synced, and I have no idea how it would even be possible to have e2e chats synced on multiple devices without having a "main" device that's doing the actual crypto or sharing the secret key