Tried with multiple textures, different prim shapes, linked prim sets, on a private region, as well as the mainland, even at a sandbox. When I log back in after one of these crashes the object does have the texture on it that I was attempting to apply.

If I stop editing the object, but do the same drag texture onto it from the inventory, everything works as expected and there is no crash.

If I keep the object selected for editing, and go through the texture tab to select the texture from the inventory, everything works as expected and the texture is applied without crashing.