they deform the ground ... do not stick to the ground we can clearly distinguish a space between the texture and the real ground.
That is most likely because they are PBR textures. Unlike the "old" ground textures used in Trainz since the earliest days, PBR textures have a height component which gives them a 3D appearance so surfaces have, for example, small rocks, pebbles, twigs, clumps of dirt, etc that actually stick up above the surface of the paint. This increases the realism of the painted surface and is not unique to Trainz as other games/sims that also use PBR textures have similar or the same issues. They are also used on the surfaces of assets.
For an example of this effect look at the foreground in the screenshot at
https://forums.auran.com/threads/australian-screenshots.189/page-1922#post-2054197
On the downside PBR ground textures do not mix well with non-PBR ground textures causing some of the effects you have noted. One solution here is to only use PBR textures. PBR textures also have problems with sudden changes in the height of the terrain, creating an effect some have called "jellyfish guts". The recommended solution there is to use plants to cover that effect.
It is claimed that fiddling with the performance and display settings in the Trainz Settings can reduce these issues but that can have other penalties.
PBR textures are loved and loathed for the reasons given above. Some refuse to use them. While others, such as myself, use them almost exclusively. You have the choice.
It is up to the creators of each PBR texture to identify that it is a PBR - usually by including the letters PBR in the texture name or its description.
There is no "magic bullet".
