Thanks, Emme, for the more detailed questions.
What is a “Cinema 4D Texture Gizmo”? Even the Help Menu has no answer to that.
The floor object (“Ground Plane”) has no UV to change, the Tiles in the Texture Tag are marked with U and V as tile direction.
PSR values can be used, but you need to know if you work with a 2D/3D shader, a fixed one (e.g., texture/image) or a procedural shader. Not everything will respond in the same way. For example: “Noise” (not simple-noise) will show the quick 2D preview in the editor, but will render a formula based result. The preview is misleading here for tiles, as the quick preview is used, not the real calculation. But not for images, there you can use it perfectly and with the Material Editor>Editor>Texture Size Preview—MB setting, change the quality itself.
However, inside of “Noise” is a “Space” set-up option, which will lead to even more options, and perhaps confusion. If you go there and chose 2D, the Tiles will work as in a quick preview, but any other setting will ignore the tile number (U/V) completely, then scale might be needed, but I would set up the main scale for noise always in the Shader itself. You might never encounter a problem, but doing it at the source of the shader feels always more healthy than later.
Typically I set no tiles, I’m not a fan of such option, as it shows (soon or later). With noise you have most of the time (not always) no repetition. If you find one, mix another noise on top to get this “healed”. I avoid “Simple Noise” and check always for the best Space settings. I often layer two or more Noise patterns, one major and anything else very “light” to be more random.
My best wishes