Oh ya, definitely easy for Blender to play tricks on your eyes if we’re looking at stuff in the 3D view haha.
And totally, at some point you’ll need a seam for more complicated geometry like the cylinder. With a bit of manual effort in the UVing as well as ensuring that the texture is actually seamless, you’d at least be able to have a texture running seamlessly across the body of the cylinder. As for the tops and bottom faces tho, that would involve a ton of work for likely sub-par results, visible seams are just a reality for that type of shape.
In these resent images, it looks like the normal map tiles correctly on the right hand plane. I’m not sure if those minor black lines in the normal map are just grid lines or if they are seams in the texture? However, the shaded plane on the right side looks correct!