I am not sure what the experience is like on a stock google pixel but I've been running the GOS Desktop Mode all morning hooked up to a USB C dock. It is quite buggy and needs a bit of love but I hope listing the bugs I've found below may help the team or other users iron things out.
Mouse Stuck On Phone: When connecting your display your mouse may remain on your phone. The solution from what I found is to rotate your phone's display or head to Settings>Connected Devices>External Display and rotate the external screen once. The mouse should be locked onto the external display thereafter.
Mouse Disappearing From External Display: This bug occurs when you open an app that prevents screenshots. At present the only solution I've found is to enable screenshots in the apps I use on a regular basis.
Keyboard Unfocused / Unable To Type On Webpages: This one is pretty odd but at times when selecting a new html input box in Vandium the onscreen keyboard toolbar will quickly flash on and off preventing you from actually focusing on the selected box and typing. For the first couple hours I would type out whatever I was intending on inputting in the address bar and then spamming ctrl v while clicking the input box but I've recently learned opening and closing the app switcher on your phone allows you to select the input box on desktop mode.
App Maximized Without Toolbar: This bug occurs when using the desktop mode window tiling/snapping feature. The left and right snapping works fine but if you snap to the top border your toolbar will be hidden. You can use Win+H to minimize the window and then open an app you haven't opened yet to return to windowed mode. If this happens to Vandium you won't be able to use html input boxes until you close and reopen the app.
Overall the experience is unusable from a practical standpoint, I'm only using it at the moment because my laptop is broken. The GOS team or Google need to work on input focus (for both keyboard and mouse) as well as add an option to disable window snapping in developer settings for it to be usable for everyday usage.