Hi @guitarvydas,
I’m not an expert on Obsidian Publish, but I have seen this behavior in other areas of Obsidian (e.g. with embedding Excalidraw drawings into slides).
The trick I use is to export the Excalidraw drawing to a PNG image, then embed the PNG image in the note instead of the Excalidraw drawing. To make this less tedious, Excalidraw has settings that will automatically create a PNG file for your drawing and update it as the drawing changes.
I hope this helps!
Craig