Thanks for the update, psussi.
There is an option to improve the setup with textures:
Subdivision> Object> Subdivide UVs: Standard/Boundary/Edge
This will fix one or the other. The triangles in the standard Sphere will challenge the setup, hence the Polygon selection. I would go another route for this.
I’m not clear if you have a linear gradient texture or a circular current in the setup.
One way would be to set the subdivision in the Sphere set up, if left as a Primitive, or use the Mesh> Add> Subdivide> Smooth Subdivide. Then create the UV newly.
Here is an example where I treaded the “pole”. The projection is set so an image of the eye can be used. A linear gradient set to spherical is a different case.
https://www.dropbox.com/s/e26zdnezuapyww6/CV3_2023_drs_22_TX_sp_11.zip?dl=0
(The eye is often simplified as one texture, but whit the “lens” as a separate object, it creates more game, i.e., splitting the cornea/sclera and iris/pupil into two objects.)
All the best