Compiled Bindings x:Bind are directives that are executed at design time to generate code to register event handlers and explicitly set the relevant properties, bypassing the {Binding} registration that uses reflection at runtime, so at runtime there is no way to detect or get a handle to the binding statement from an x:Bind because there is none.
As partially explained by @Jayden, it is not necessary to obtain the binding at all in your specific case, as it is not necessary to manually/explicity call update on the binding when the text is changed, to do so is counter intuitive and leads to unexpected results.
The correct way to ensure that immediate changes to the Text property of a TextBox are comitted back through a traditional TwoWay {Binding} or a compiled TwoWay {x:Bind} is by setting the UpdateSourceTrigger=PropertyChanged.
in UWP, both {Binding}and {X:Bind} support UpdatteSourceTrigger, however {X:Bind} has a simpler implentation with limited options, however both do support PropertyChanged
Both of the following would work:
<TextBox Text="{Binding Name, Mode=TwoWay, UpdateSourceTrigger=PropertyChanged}"
Width="200"
Margin="5" />
<TextBox Text="{x:Bind VM.Name, Mode=TwoWay, UpdateSourceTrigger=PropertyChanged}"
Width="200"
Margin="5" />
The ONLY time that you would manually update the binding is if your binding statement has set the UpdateSourceTrigger to Explicit.
The reason that you should not try to manually update binding is because it will conflict with the binding statement, especially if the binding is deliberately set to UpdateSourceTrigger=LostFocus. In this case your event handler will still update the binding on text change, when or if this becomes a problem for developers in the future they will not think to look for explicit handling of the text changed event
As part of a migration to compiled bindings x:Bind and acknowledging that they could be used for any bindings, you should carefully review all calls to GetBindingExpression() in your code and try to elminate them as GetBindingExpression() is no longer a reliable mechanism to determine if a DependencyProperty has been configured, or to get the binding statement for a DependencyProperty at runtime.
I am aware of one standard control (NumberBox) that does not properly support UpdateSourceTrigger=PropertyChanged, however due to the fact that you cannot determine if a compiled binding has been used to bind a property other solutions need to be used to affect the changes that we are expecting, see this post for solutions to NumberBox