Hi HaxO,
When using movable lighting you’ll want to adjust the select the movable light(s) in question and adjust the shadow bias and possibly the shadow filter sharpness to get the desired results.
Here is my example of your setup.
In this scene I’m using a wall with a 3d text mesh that is recessed slightly into the wall with 3 spot lights set to movable.
Here is the default settings results:
Shadow bias: 0.5 and Shadow Filter Sharpness: 0.0
Here is the adjusted settings results:
Shadow bias: 0.1 and Shadow Filter Sharpness: 0.2
If you noticed in the bottom you’ll start to see some banding with lines running horizontally across the image. This is to be expected and is a result of taking the shadow bias that low. The way to correct this is to use Shadow Filter Sharpness at a higher value to correct but you lose softer shadows. There is a trade off here when using these two settings to get the best results.
This is not settings to use but for demonstration
Here is the adjusted settings results:
Shadow bias: 0.0 and Shadow Filter Sharpness: 5.0
I would like to suggest another method that was introduce with 4.5 though.
Ray Traced Distance Field Soft Shadows
With this you will be able to control the shadow sharpness by the source radius (low values work) and in the mesh editor under build settings in the details panel you can change the Distance Field Resolution scale to get better results for shadow quality. Default is 1. For this example I set it to 3 to get better results.
Reset all other settings back to default (doesn’t really matter) and enable the Ray Traced Distance Field Shadows check box for the movable light.
Here is the documentation: Distance Field Soft Shadows in Unreal Engine | Unreal Engine 5.1 Documentation
This is a twitch stream demonstration that is well worth the half hour to watch: - YouTube
If you have any questions feel free to ask. I don’t mind offering some tips to get the best results! 
Tim