Is there a way to increase Rendered texture resolution same as UV mapping?

As shown in the screenshot the UVEditor texture mapping resolution is much detail than Rendered

For example, presentations are made up in Rendered mode, not in UVEditor mode.
Looks like a UI bug but before reporting as so I wish to have more understanding.

Is there a way to increase the Rendered resolution?Rhino Bug- UV mapping resolution III Vr01.3dm (4.8 MB)

Also, there is no way to export this in FBX with correct UV mapping. So I’m wondering if the low rendered resolution is somehow affecting the UV mapping.