I have an image that is placed over a white solid background "color clip".

Now I'd like to blur the entire combination of image and background. In other words, I'd like to first combine background and image, and then apply the "blur" filter to the resulting frames, not to image and background separately.

However, I do not manage to achieve that. If I add a "blur" filter to the image, a dark border appears because the blur operation assumes black pixels outside of the image, and these contribute to the calculated blurred pixels (but I'd like the white background pixels to be used instead). I also tried to group the background and the image and apply the filter to this combination, but this does not change the result.

So my question is: How do I apply an operation the the "already processed frame stack"?

you can apply an effect on all track (maybe too much?) placing it on the "MASTER" stack.

That will not work in my case. My intention was to blur a background and then put another image on top.

Since the tracks are stacked and there is a z-order, it would be good to be able to apply an effect to all layers underneath.

With some filters it is a real problem that this cannot be done. For example, the blur filter results in edge artifacts, A white rectangle layer that is blurred will get dark edges because the pixels outside the video object are assumed to be black - even if the displayed background is white. If it would be possible to first superimpose the rectangle (or whatever) on the white background, and blur the combination of the two, the gray edge would not occur.

Let me try to understand what you want to achieve:
You have a white background and an image on top. When you blur the image there will be hard edges against the white background. You want the entire screen blurred which essentially would give a soft edge between the image and the white background.

Assuming this is what you want to achieve here is how you can do it (it is not perfect but perhaps gets you close enough):
Have your white color clip in track V1, the image above it in track V2. Add a transform effect to the image to bring it to the size and position you want. Add a blur effect to the image (I am using Gaussian with amount around 600-700). Add a rectangular alpha mask to the image and fiddle with the settings.

Example (project is HD 1080p) settings for a nice soft edge (feathered) appearance:
Image size 2560x1440
Transform effect to reduce image size by 50%, centered
Blur effect whatever
Rectangular Alpha mask effect left=263, right=263, top=263, bottom=263, blur=15

Hope this helps