I don't know if this is my config or the default, but on my machine those features are set up like this:
- Multiple desktops: Winkey (list) or ctrl+alt+arrow (left and right) or triple finger drag on the trackpad (wayland)
- Move app to next screen: I know this is possible to configure, don't know the key combo, I move windows between virtual desktops more often
- Move app to next desktop ctrl+alt+shift+arrow keys (similar to switching desktops)
- Switch windows: alt+tab
- Switch windows in app: alt+tilde
- Launch program: alt+F2
- Vertical task bar with widgets: not without a bunch of extensions. You're stuck with a horizontal one in the vanilla config. I've enjoyed the default config Manjaro ships for Gnome myself, which provides a more fully featured task bar than the default setup, so maybe there's an extension that's right for you.
- Windows always on top toggle: in the window menu (when you right click on the window chrome)
- Volume up/down: bound to media keys by default, but I'm sure you can configure the necessary shortcuts. I'd probably bind a shortcut that injects media keys (xdotool?) to ensure compatibility with other programs but you could set up a shortcut to your favourite audio manager if you wish
I don't know about a searchable window list or launching a program always on top. You can configure a shortcut to mark a window as always on top after launching, and for the window list there's probably an extension out there (this seems promising https://extensions.gnome.org/extension/1001/window-search-pr...).
Opening a window on a specific desktop should be possible with extensions (I think https://extensions.gnome.org/extension/16/auto-move-windows/ does this?)