Ok, now I get it.
The dropdown menu's option generates a filter named Blend. Opened with the filter editor, the names are listed on the left, next to checkboxes and a number showing how many objects have the same filter.
When you select the filtered object, you also select the filter in the filter editor, so the "node-based editor" part of the filter editor panel should be active then.
That is the part saying effects, connections and the listed sources.
Every filter primitives in the filter chain is listed below the "Effects" in a cloumn, one after another.
The Fill and Transparency/Blend... filter only consisting of 1 filter primitive.
The "image" option doesn't really affect any other object in the svg document, it only blends the original object upon itself.
The other option with the "background" is broken as mentioned above -you need a layer with a custom blending mode in the document once to enable it working, though that enabling persists even after such a layer is deleted (if cleanup file/vacuum defs isn't run.)
How to make the real "image" work to use another object in the document.
Create a new filter definition it the left panel where they are listed, name it for example ">>blendimage<<".
Then, at the "Add Effect" list choose "Image" filter primitive.
Select the object you want to pull in from the file and in the "Effects parameters" click the "Select SVG Element" button.
That will show the selected object's id in the effect parameters box, like "#rect3699".
Then, add a blend filter primitive from the Add Effect" as before.
The first connector pulls in the top and the second the bottom input for the blending.
If you want to blend the filtered object on the top of the pulled in object, then the blend primitive's first connector needs to be connected with the source graphic on the right and with the image filter primitive with the second connector.
Then in the filter general settings set coordinates 0, 0 and dimensions 1, 1.
Done.
Now, to apply the custom filter on an object, select the object and tick in the filter definition's box in the filter editor.
Be careful as if you apply this filter on the pulled in object, that creates the instant crash as mentioned above.
-The pulled in object would be blend onto the pulled in object, pulled in again and again in an endless cycle. "Cross referencing".-
Attaching an example with the final result.