Thanks for your replies! I did a lot of testing and experimenting, but sadly I’m not quite there jet…
@labris. Thanks for the playground! I also tested your approach, but unfortunately when I want the blurry parts to update in realtime it seems to be not performant enough. 
(same when I tryed DumpFramebuffer instead of Screenshot)
I’m not quite sure about the second-camera-approch you guys described. How could I attach the RTT or the camera to the GUI this way? Or would I not do this and use the RTT as texture on a plane and set it as a “background” for the second camera, putting the GUI on top?
When setting up a plane and giving it a rtt-material it isn’t more performant, than the approach I used based on this playground https://www.babylonjs-playground.com/#KG6SGU#13 by @Gijs, where I am able to paint the RTT directly into the GUI. (Via: How to show a RenderTargetTexture on GUI?)
However, sadly, when I use this approach, I get this nasty edge-glitches… I assume it has something to do with the custom shader used…?
Even more sadly it appears I’m not competent enough to remove the whole greenscreen-custom-shader-thingie and just display the RTT without any shader 
This playground (https://www.babylonjs-playground.com/#5E96NN#2 // https://croncle.blob.core.windows.net/playground/renderTargetTextureImage.js) mentioned earlier in said discussion seams to be exactly what I want - unfortunately it is somehow broken, my firefox tells me “Uncaught DOMException: An attempt was made to use an object that is not, or is no longer, usable”… And again I’m not competent enough to fix it
So my conclusion so far: it is possible to display a RTT within a GUI.
It also should be possible to set the image.source to a base64 output of the RTT (similar to what @labris suggested), but probably it is not very performant as a base64 would be rendert for every frame, correct?
As far as I understand @Gijs approach, the RTT doesn’t get rendert, rather transformed into a 2d-representation an integrated into the GUI?