There's no perfect way to change the user agent string for the UWP WebView (x-ms-webview in HTML, Windows.UI.Xaml.Controls.WebView in XAML, and Windows.Web.UI.Interop.WebViewControl in Win32) but there are two imperfect methods folks end up using.
The first is to call UrlMkSetSessionOption. This is an old public API that allows you to configure various arcane options including one that is the default user agent string for requests running through urlmon. This API is allowed by the Microsoft Store for UWP apps. The change it applies is process wide which has two potential drawbacks. If you want to be able to have different UA strings set for different requests from a WebView that's not really possible with this solution. The other drawback is if you're using out of process WebView, you need to ensure you're calling into UrlMkSetSessionOption in the WebView's process. You'll need to write third party WinRT that calls UrlMkSetSessionOption, create the out of proc WebView, navigate it to some trusted local page, use AddWebAllowedObject or provide that URI WinRT access, and call into your third party WinRT. You'll need to do that for any new WebView process you create.
The second less generally applicable solution is to use NavigateWithHttpRequestMessage and set the User-Agent HTTP header. In this case you get to control the scope of the user agent string changes but has the limitations that not all sub resource downloads will use this user agent string and for navigations you don't initiate you have to manually intercept and re-request being careful to transfer over all POST body state and HTTP headers correctly. That last part is not actually possible for iframes.
The GoBack and GoForward methods on the UWP WebView (x-ms-webview in HTML, Windows.UI.Xaml.Controls.WebView in XAML, and Windows.Web.UI.Interop.WebViewControl in Win32) act the same as the Back and Forward buttons in the Edge browser. They don't necessarily change the top level document of the WebView. If inside the webview an iframe navigates then that navigation will be recorded in the forward/back history and the GoBack / GoForward call may result in navigating that iframe. This makes sense as an end user using the Edge browser since if I click a link to navigate one place and then hit Back I expect to sort of undo that most recent navigation regardless of if that navigation happened in an iframe or the top level document.
If that doesn't make sense for your application and you want to navigate forward or back ignoring iframe navigates, unfortunately there's no perfect workaround.
One workaround could be to try calling GoBack and then checking if a FrameNavigationStarting event fires or a NavigationStarting event fires. If a frame navigates then try calling GoBack again. There could be async races in this case since other navigates could come in and send you the wrong signal and interrupt your multi step GoBack operation.
You could also try keeping track of all top level document navigations and manually navigate back to the URIs you care about. However, GoBack and GoForward also restore some amount of user state (form fills etc) in addition to navigating. Manually calling navigate will not give this same behavior.