I have decided not to get into electronics this time and just bought 2 wireless chargers at IKEA, which are a bargain at 5$ a piece. They are made in a regular cylindrical shape, which makes it easy to integrate them.
When it came to 3D printing, I happened to have a ColorFabb WoodFill filament laying around, which I couldn't find any use for. The print turned out pretty good, looking somehing like machined MDF from a distance. The two sides are connected together with two M3 screws and nuts. Later on, it has been decided not to use screws to attach the holder to the wall, hence the hook-and-loop like tape in the corners.
I made the 3D model in Fusion 360 and it is optimized for the Pixel 3 XL phone. Smaller phones will fall out, but is should easy to adjust in the model. Two sides are assymetric, with the intention to have a gap hidden. The Fusion 360, STEP and STL files are free to download.