Default AWS WorkSpaces Windows Client to Windowed Mode every sign on

In light your request, I checked that as per the below reference, the window view needs to be manually changed:

https://docs.aws.amazon.com/workspaces/latest/userguide/amazon-workspaces-windows-client.html#windows_views

As per this:

You can switch to full screen mode by choosing View > Enter Full Screen (3.0+ clients) or View > Show Fullscreen (1.0+ and 2.0+ clients) in the client application menu. While in full screen mode, you can switch back to window mode by moving the pointer to the top of the screen. The client application menu is displayed, and you can choose View, Leave Full Screen (3.0+ clients) or View, Exit Fullscreen (1.0+ and 2.0+ clients) in the client application menu. You can also toggle full screen mode by pressing Ctrl+Alt+Enter.

As there are no default options to set this to windowed mode, it currently will require this manual input to update the same. Keeping your concern in check, as you have rightly inferred, you may reach out to the AWS Premium Support Engineers via Support Case and request for an input on this request and log a feature request on it as well.