Yes it does repeat, I’ve shown you a very large zoomed version. Here’s how it looks when tiled.
It looks weird at the edges but if that is taken care of, it looks pretty good I think.
If you can visibly see the border, it doesn’t tile well. Maybe redraw it in tiled mode, where the canvas repeats while you draw (not sure if you have that in inkscape).
What? The edges don’t look weird at all, what are you talking about? Your tiles are perfectly usable :