Hi. It's super easy really. Just add a dockpane with a WebBrowser control in it. Then instead of opening a browser just assign the url to the dockpane WebBrowser.
//Open the dockpane if it isn't already open
DockPane pane = FrameworkApplication.DockPaneManager.Find("ArcPro_DSM_Settings_Dockpane");
pane.Activate();
//Access the web control through the View
DockpaneView myView = DockpaneView.MyDockpaneView;
myView.currentUri = new Uri(@"https://www.google.com/maps/@?api=1&map_action=pano&viewpoint=" + lat + "," + lng);
myView.streetViewControl.Navigate(@"https://www.google.com/maps/@?api=1&map_action=pano&viewpoint=" + lat + "," + lng);