I am thus wondering how such 3D (3×3×10 in my toy example) convolution filters are usually displayed as 2D images (i.e. sum or mean, ...)?
TL;DR The 3x3x10 image is displayed as 10 3x3 images
Say you start with a 32x32x3 image
You decide to use a filter of shape 5x5x3 with an output depth of 15 (with no padding and stride 1).
i.e., you will convert the 32x32x3 image to a 28x28x15 image.
What does this depth of 15 really mean?
Each of the 15 dimensions represents one filters output.
i.e., when we apply an output depth of 15 for a 5x5x3 filter, we take 15 5x5x3 filters and apply them to the image. From them, we get 15 28x28x1 images.
Each of these 15 $28$$\times$$28$$\times$$1$ images are stacked on top of each other to make a 28x28x15 image.
So, to answer your question : the $N$$\times$$N$$\times$$15$ images are split into 15 NxNX1 images and displayed.
Note: you'll notice in many CNN visualisations as the depth of the convolutional pyranmid increases, the number of small images increases.