I’m not sure if there’s a specific size that can fit all backgrounds. I visited your project Strife: The Expanse on Firefox, I resized the window so it’s very wide (going beyond the screen) and I could see the background repeating and the line of its limit.
My suggestion would be, your background is already hexes, make it repeatable. As in, the same hexes that appear when the image starts, should appear when the image ends. I’m not sure if the colors are meant to display a specific pattern, but this technique would ensure your background looks descent on all screen sizes.