Why do my tires look like this?

That doesn't look like any suspension or alignment issue, it looks like a very soft compound tire being run on a rough pavement or gravel surface, with that chewing out small pieces of the tire as you corner and drive. Sort of like using a rough sandpaper on soft wood. Being those are well worn Kuhmos I would say you have worn through the harder tread compound of the tire and now that they are worn the softer inner compound is showing because the lack of the rain grooves and siping are being offset by the grip of the softer material. Sort of like the way a snow tire works, the softer compound allows the tire better grip but at the expense of tire wear.
Suspension issues usually show as other wear patterns like cupping which is from bad struts or shocks or even balance issues. Then there is feathering which happens if the tire is leaning or towed in or out. In that the tread will look like saw teeth and things like center or outer shoulder wear from over or under inflation.

While it's possible hitting the rodent did damage, unless it was very severe the wear wouldn't show that quickly.

From what is shown I doubt you have any issues, however, depending on where you get your tires from a good shop will inspect the suspension for issues and will likely want to do an alignment check at the least. That is actually a good practice with new tires as many tire warranties specify that alignment be checked when they are installed or the warranty is void. Plus many of the better shops will offer repairs and rotations with the purchase price of the tires.