I think the flaw in your design is to create the OLE object directly from Writer. You won’t be able to control all properties of the object, not to select the really significant part in the slide.
What you want is not the full embedded document where you insert it, but some of the shapes you have drawn. Transparency do not apply to embedded documents, only drawing objects or frames. Document embedding hides the objects it contains.
My recommendation if to make your diagrams and other illustration in a separate Draw document. Consider it as a “gallery” of various illustrations. You select with the mouse the set of shapes you need (ideally, you merge them in a group so that a simple click will select the whole group), then you copy them (
C) and you paste them (
V) in Writer at the appropriate location. With this procedure, where ther is nothing in the Writer frame, this ‘nothing’ is transparent. If your shape have a background, the background is kept (of course, when the background is set to None the shape is transparent and only its border and label will show). Additionally, the whole Writer frame can have a transparency attribute, which is honoured in this case.
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PS: I gave a careful look at your document. Its structure is a mess. You have 14 frames with text (some of which nested inside another one) in 2 pages. You seem to position the frames with empty paragraphs (the same techique is used inside the frames), which is nonsense (not to speak of horizontal positioning with tab characters plus spaces) and will defeat any attempt to format the doc in a smart way.
If your document must adhere to some predefined format where the page is the primary focus, not text (this is the case for ad flyer or sale documents), then you should try Impress (but not easy) or Draw speaking about the LibreOffice suite at your disposal or go with Scribus, a libre desktop publishing application which puts it emphasis on page and blocks within pages. Writer focuses on managing a text flow which automatically spans as many pages as needed.