Just an update from my side:
I implemented it now by always use a scaling factor of 1 for rendering the tilemap to a render target.
The render target is then scaled according to the scaling factor of the camera to enable zooming.
First it worked fine. But later I have seen, that in some rare cases, when the camera position became very strage (non integer numbers anymore), the error appeared again. I could fix this by rounding the position of the camera to integer values before creating the transformation matrix for the tilemap rendering. Now the error is not visible anymore.
However, I think the idea of still using a padding with pixels of the same color as the adjacent pixel of the tiles is a good fallback, in case that any user manages to get strange camera positions again. So the combination of both solutions might be a good choice. Or later I will build up a tilemap from a mesh and can solve the issue as suggested in the posts from will_2021 and MystricRiverGames.
Thanks a lot for your assistance and suggestions.