Hi Johnnymycat,
Welcome to Affinity Forums :)
Currently there's no way to dynamically apply a blurry effect to an underlaying layer but you can fake it using the Layer Effects as @crabtrem suggested.
I've attached a sample file for inspection below.
Assuming you already have an image as background:
1- first draw the shape you want to use to blurry the background;
2- duplicate the bacground image and drag it over the shape in the Layers panel (NOT over its thumbnail but over the area on the right otherwise it will not work). We are using the shape as a clipping layer for the background, so only the part of the image that lays inside the rectangle is visible. To avoid this duplicate changing it's position in relation to the "real background" select the shape layer, go to the context toolbar and check Lock children.
3 - with the shape layer still selected click on the Layer Effect (FX icon) button on the bottom of the Layers panel and check/select the Gaussian Blur. The value you have to apply it varies depending on the size of your image, so adjust it until you are happy with the result. Make sure you check Preserve alpha to apply the FX up to the boundaries of the shape.
That's it. You can now move the shape and it will "fake" a dynamic blur being applied to the image as long as you don't add new objects between the shape and the background image.
blurry_effect.afdesign
Have you tried using the FX on the rectangular object? There is a Gaussian Blur FX, along with some others you might also consider. You could also place a Live Filter on the rectangle too. But I find the FX are often overlooked and under appreciated.
