What exact breed of animal is a 金丝熊?
Officially, it is "Mesocricetus auratus" (Golden hamster) (source1 source2). It belong to "仓鼠科", and it should a kind of "鼠类" in Chinese.

However, as not everybody is a biologist, and as the name for it is "金丝*熊*", it may not be treated as mouse in everyday life.

Another reason is that "鼠" does not carry a good meaning in Chinese. It is often related to "stealing" or something alike. So it may be avoided to name a kind pet animal. (However, we do have "仓鼠" for pets.)

btw: To be honest, I've never seen a real "金丝熊".