Hello,
Welcome to Microsoft Q&A!
Based on your words, you are having an issue that the binding source is not updated on time when the text is changed in the TextBox. It's not the best practice to set focus state for the TextBox to update the binding source. The root problem is that the binding source should be updated on time. For this issue, UWP has a special property that could solve the issue directly.
Please try to check the Binding.UpdateSourceTrigger Property, this property determines the timing of binding source updates for two-way bindings. You could set the property to PropertyChanged, it means the binding source is updated whenever the binding target value changes. After you set it, the binding source will be updated once the text is changed instead of when the TextBox loses focus.
You could use it like this:
<TextBox x:Name="MyTextBox" Width="500" Height="300" TextChanged="MyTextBox_TextChanged" Text="{Binding MyText,Mode=TwoWay,UpdateSourceTrigger=PropertyChanged}"/>
Thank you.