I have gradient noise that is being used to offset the vertex shader over time, but I want to use this noise to also add distortion to the base color which is currently the scene color, in order to make it look like moving water. Is it possible to convert the noise into a texture? Or would there be a better way to do this?
To the explicit question of “is it possible to convert something into a texture in Shader Graph” the answer is no. Shader Graph can move or otherwise modify a mesh’s vertex positions and output a per-pixel color in the areas that mesh is visible. It cannot create a texture, but there’s also not really a need to do this.
If you want to use the Gradient Noise node to modify the base color there’s not anything special you need to do apart from connect the output of that node to the nodes that connect to the master stack’s color.
If you want it to be only those values that are calculated per-vertex, then you’d need to create a custom interpolator on the Vertex master stack to pass data from the vertex to the fragment shader stages of the shader.
https://docs.unity.cn/Packages/com.unity.shadergraph@12.0/manual/Custom-Interpolators.html
This is something that was added in Shader Graph 12, so you’d need to be using Unity 2021.2 and URP or HDRP 12 to get access to it.