Nope, and that’s the biggest blocker for me. I own multiple smart phones (work and personal), iPad, and two computers (windows and Mac). So far Facebook messenger is the only reliable way to do messaging across all of them, which is a shame because I hate Facebook and I don’t particularly like messenger. But I have not found a single other solution that works cross-device and cross-platform. It also helps that basically everyone is on Facebook messenger, but I’d be willing to put effort into trying to migrate people to other chat solutions if there was literally anything else out there that works well on multiple devices.

Telegram

I use Element (Matrix) on Ubuntu, Windows 10, and Android. It works great so far, with a few exceptions such as sharing videos from reddit, for example.

Nope. You can't even use it on a tablet without owning a smartphone.

So is the model similar to that of WhatsApp web? can you receive messages on the desktop app if your phone is switched off?

Unlike WhatsApp, the desktop app receives messages when the phone is off. Also unlike WhatsApp, messages received on the phone before you paired the desktop app do not get transferred to the computer.

It’s open protocol and source though, so making a multi-device version wouldn’t be impossible