A combination of Google Assistant, Talkback, USB-C-to-USB-A-Adapter and Keyboard, a Bluetooth keyboard, scrcpy, Anydesk and a new Pixel phone for practicing helped get some data off the device and even do a migration to the new phone. Needed all of the above and a lot of trial and error and time!!
I do most of my meetings on my phone, and enlarging the screen if someone is sharing their screen works pretty well (it's not perfect, but more than enough for presentations). But I can of course transfer the call to my PC if need be.
But I just have scrcpy up in a window on one of my screens/workspace constantly. The keyboard shortcuts work quite well and I don't have to break my flow just to do something on my phone. Clipboard is synced as well.
If I get a notification I can check what it is about without taking my hands of my keyboard etc.
I'm sure it sounds a bit convoluted, and each usecase (meetings, notifications etc.) have other better/more-native solutions but the experience all in all is a game-changer.
To the point where "just picking up your device" is too much of a bother. Why not do it through scrcpy instead? Quicker, proper keyboard etc. and the mouse works really well. To the point where I kind of miss right-click is "back" when I'm outside the scrcpy window.
For your last point, there are many mice with 2+ side buttons, which are mapped as forward and back by default and can typically be remapped, it works in pretty much any application that has a "back" option.
Don't feel it is the same, because desktop applications don't work the same. And when you are on the "last screen" and press back on a phone you get to the home-screen. So in most cases a single tap or double-tap takes me to the home-screen.
So it is both for going back and "quitting" applications.
On the desktop it wouldn't even work in the browser, because I work by tabbing new pages and closing tabs rather than navigating back.
So to be fair, I don't want it om my desktop. Because I really don't want my applications to mimic the behavior they do on phones, that would be horrible. But the end result is really nice for the weird usecase of running a phone inside a desktop.
What do you use it for that makes it better than just picking up your device?