alright to divert away from anything irrelevant to OP, and hopefully add some helpful or comforting thoughts.
My friend had a cat go missing in a small city in Alberta (very cold) - he moved away several months or more than a year.. i cant remember... and several months after moving "to the other side of the city" the cat showed up on their door, scruffy as all hell. "meow"
idk if its been mentioned... make a pendulum? ouija board?
Oooh i just had an idea.. you could sit with some cardstock or something, go nab some business cards from some banks clerk and steal a sharpie if you cant afford supplies, and sit and breathe deep and think about possible places the cat could be, write down any ideas that flow through your head. you could write some distances and directions down, whatever comes to mind as something that could possibly be true (for example, its unlikely the cat drove a car, boarded a plane and is currently in vegas doing drugs) - write all these things on cards and start drawing them like tarot cards.....
I feel ive been negligent in my devotion by failing to mention to ask Hecate. She once brought a lost cat to me. Also shes holder of the keys between worlds and timelines. Make an offering

oh she likes fish too - a cat connection i'd never made - if you want to make an offering, but she also loves garlic (hummus!) and honey cakes

i hope you find your cat