Hi Alexey,
Thank you for contacting Syncfusion Support.
In SfTextBoxExt, you can apply visual style using our Themes Studio. We have created a sample with SfTextBoxExt control. In this sample, we have created VisualStyle using Syncfusion Themes Studio and added in ResourceDictionary. Please download the sample from the below link.
Sample:
SfTextBoxExtThemeSampleWe also like to add that "SkinStorage" is used to apply style for classic controls and not for "Sf" controls. So, we recommend you to use our Syncfusion Themes studio for "Sf" controls.
Regards,
Venkateshwaran V.R.