Can I activate the cat?
you can find the mouse in the gem store but only after making a purchase (after viewing a short cut-scene). once caught, bring it to the cat, and then it will join you to fight as a pet with you in battle - you can also upgrade the cat over time.
Also, the cat on top of the restaurant will tell you about its dream of catching a mouse. That’s all the cat does – it’s there for decoration. No secret usage unfortunately.
Source: PPKP – Answers and Spoilers