There is no place for a transparent "color" in the common video formats/encoders, so you have to pick and declare one of the existing colors as "transparent". For example some kind of green. Create an image filled with exactly this green and use this as bottom source in OBS. Now, videos you create have this green in places where you want it to be transparent.
In the app you want to use this video, you need a feature to convert this color to transparent. In OBS, you do this with the color key filter. Apply it to the media source where you play the video created above. It's somewhat similar to the green screen technique used in movie production. (In case of real green screens, you rather use chroma key filter instead of color key filter to allow for regions of different brightness of a actual green screen due to the lighting).
The color does not need to be green. Choose any color you like, preferable a color that isn't contained in the actual video, so you don't accidentally make parts of the video transparent you want not to be transparent.