Triban is a bike brand, so not particularly relevant here. Bike manufacturers assemble parts from component manufacturers. The most prominent of those, Shimano, make your chainset, and Triban are just one of hundreds or thousands of bike brands using identical Shimano products. Other posters are correct: the important thing is which generation of Sora chainset you have, because the Sora model name has been used for decades, I believe since 7-speed.
If I read your post correctly, you're saying that you have 9-speed Sora. If that's
this chainset here, that same page lists chainrings to match (although the larger ring costs half the price of a whole new set). This is just one (very good) bike shop, and you'd be able to get the rings in loads of other places.
If that's the wrong generation of Sora chainset, we need to identify the correct one as a first step. Photographs, and/or the model numbers off the front or back of the cranks, would be the only reliable way to do that.
As a general answer, you can fit other brands of ring to your cranks, but the BCD (bolt circle diameter) - the diameter of a circle through the bolts that secure the rings in place) must be correct, as that varies between brands and models. It's often engraved into the rings. Also, newer Shimano chainsets tend to have four arms, whereas most older ones from most manufacturers have five. Pretty obviously, you can't mix and match between four and five! You probably know that, because you talk about making the styling match, which would require Shimano rings.
Hope this doesn't sound overly fussy as an answer. It's just not possible to help without this information.
By the way, I don't think I've ever heard of a cracked ring before. What happened? Usually it's just worn-out teeth. A photo of that crack might help too.
