Is there a way to connect the density/width control to the x-axis control of the texture scaling?
Also if you find some major flaws in the geo setup feel free to tell it :)
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Since you unfortunately didn't share your blend file with us, I can only show you with an abstracted example:
First, I instantiate a grid with dimensions 1x1 along a mesh line.
I use the distance of the points at the same time as a scaling factor for the instances.
Additionally I capture this value with
Store Named Attribute in the Face Corner domain of the geometry.
This scale factor is then read in the shader with the node
Attribute, and the texture coordinates is multiplied with it.