You’re very welcome, Felix.
You can control drag the Material tag in the object manager and adjust this projection again. As often as you like.
This ensures a certain resolution based quality. If it is pasted on a basic texture on the object, a change of quality will happen (or the underlying texture is massive.)
I own a book about unwrapping the earth. (Flattening the Earth: Two Thousand Years of Map Projections Two Thousand Years of Map Projections Snyder, John P.), which I have used extensively to create a long time series in my photographic art. Going through 2000 years of trying to unwrap the Earth to a map has shown clearly that there is no one size fits all options.
I mention this here, as the method of projecting and pasting anything to a texture based on a more or less complex object is not trivial.
The most popular option is Mercato or Equirectangular. Even those distort the shapes. Will say, any paste of a single object onto a final “map” (the resulting texture) will paste the single images on areas with higher or much lower resolutions. As a side effect, the quality can only be kept alive if the underlying texture is at its lowest resolution, at least 1.5 times higher than the pasted texture (relative to the surface area of the object).
Having a good UV skill helps to avoid those super high resolutions while keeping the quality (more or less) constant. The target of UV is to distribute the texture pixels equally to the surface while allowing a texture with the least distortion amount. This is, of course, the ideal case. The more complex a geometry is, the less likely this can happen. Here, the standard example is how to wrap an orange (or Earth) with a single sheet of paper.
Any texture has some kind of way to be positioned on a surface. This is called projection. This projection can be turned with a single mouse-click into UV information. Given that, the projection with copy and paste is possible in BodyPaint 3D, but since you need to avoid this, I have and will not suggest this.
Here is an illustration of the process (Projection painting and the Layer Manager.)
https://help.maxon.net/r23/en-us/Default.htm#html/11680.html?TocPath=BodyPaint 3D|Tools Menu|Projection Painting|_____0
Please note, that BodyPaint 3D can work with standard projections to a certain degree.
https://help.maxon.net/r23/en-us/Default.htm#html/11568.html?TocPath=BodyPaint 3D|First Steps|_____2
If I know why UV can’t be used, I might understand the problem better.
As I have seen how quickly I can introduce this skill in a hands-on class, the response in the class was mostly:
To have been avoiding this for so long has cost me more time (finding workarounds) than to learn it.
I assume it is based on something else that I’m not aware of; Perhaps pipeline based?
For your exploration, my best wishes.