Look at background layers first
A white layer can make a PNG opaque even when the file format supports transparency. Inspect the PSD’s visible background layers and the canvas edges. Use a copy when changing layer visibility for an export.
Choose PNG for transparent output
Use File → Export → Export As and complete the PNG download. JPEG does not preserve an alpha channel. Saving as PNG allows transparency, but it does not remove an unwanted visible background by itself.
View the result against two backgrounds
Open the downloaded file and inspect it against light and dark backgrounds. Look for halos, rough edges and unexpected opaque areas. A thumbnail on a white page can hide a white background that should have been transparent.
Keep the layered document for refinement
If the edge needs another change, return to the working PSD rather than editing only the flat export. Keep the PNG as a delivery copy and the PSD as the place for revisions.
Source
Application details: PhotoCraft official application page and version 0.7.0 hosting guide.
Questions, answered.
Does choosing PNG automatically remove the background?
No. PNG can preserve transparent pixels; it does not automatically turn a visible background into transparency.
Can JPEG keep a transparent cutout?
No. Use a format with an alpha channel such as PNG when transparency is required.
Does transparency mean the file has editable layers?
No. A flat PNG can have transparent pixels without PSD layer structure.