More specifically, I typically need to convert an image with a white background to have a transparent background so that it blends more naturally with a non-white background.

If you place an image that is PNG with a transparent background. The image will show a white background. If you place an image with its own background, it will cover the white document background.

To change a black background to white in Microsoft Word, open Word, go to the Design tab, and select Page Color. Now, from the dropdown, select the White color.