Thank you for the clarifications.
Does this mean that we have to swap development to some other framework in order to use features in your SDK?
No, you can use WinForms and .NET framework. Since drag and drop page re-ordering is not built-in, then this is a customization you would add in your own UI.
You would use SetupThumbnails and GetThumbAsync to get the images you need for your custom control.
https://www.pdftron.com/api/PDFTronSDK/dotnet/pdftron.PDF.PDFViewCtrl.html#pdftron_PDF_PDFViewCtrl_SetupThumbnails_System_Boolean_System_Boolean_System_Boolean_System_Int32_System_UInt32_System_Double_
https://www.pdftron.com/api/PDFTronSDK/dotnet/pdftron.PDF.PDFViewCtrl.html#pdftron_PDF_PDFViewCtrl_GetThumbAsync_System_Int32_pdftron_PDF_PDFViewThumbAsyncDelegate_System_Object_
Then when it is time to apply the edit, you would use PDFDoc locking to write lock and unlock.
Then edit the PDF, see this sample for page editing logic.
Finally after unlocking the PDFDoc, you would tell PDFViewCtrl to update to reflect the new layout using this API.
https://www.pdftron.com/api/PDFTronSDK/dotnet/pdftron.PDF.PDFViewCtrl.html#pdftron_PDF_PDFViewCtrl_UpdatePageLayout
Here is a forum post showing a minimal example.
Let me know how this works for you.