If the first screenshot is your pattern then yes, you will end up with seams because first and last cows are at the edge of repeating pattern. Omit cow in the first column if you want seamless pattern or space cows differently.
Regarding PPI. If you need pattern for Web do not change anything, on the internet PPI does not play any role, it will be ignored. Otherwise do not save using Export As or Save for Web but rather using Save a Copy.
The actual seamless tile for your pattern seems to be 1025px x 1025px.
As 3600 is not an integer multiple of 1025 it should not tile seamlessy at that size unless scaled.
I started with a 1024 x 1024 midjourney image. The goal is a 12 x 12 inch seamless pattern (300 dpi). I upscaled it x 2 and created the pattern in Photoshop which results in a seamless pattern but as soon as I modify the size to 12 x 12 inches, the seams appear. I'm stumped as to how I to achieve the desired result. Any guidance would be greatly appreciated!!
• Either scale the tile according to the intended final tile-dimensions
• or the sides of the ultimate format need to be integer multiples of the original tile’s sides.
How often is the image supposed to repeat along the 12 inches?
12in at 300ppi means 3600px, so the tile needs to be 3600px/x wide/high with x being the number of repetitions.
If you want the tile repeated 4 times that means 3600px/4 = 900px.