The domestic cat has a range of up to 10 km per day
this is significantly shorter than human which are excellent migrants, can sustain maybe 30 km per day.
At 10 km/day it would take a cat about 11 billion years to walk to alpha Centauri.
Which unfortunately would have burned out by then.
But since humans would have got there about 8 billion years earlier, we'd no doubt leave some crunchies and a bowl of fresh water around proxima Centauri
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Is that their range because of physical limitations or because they are bored?
Just a lazy google...
Near as I can tell it is the upper limit of observed ranging by wild domestic European felines.
Should be a decent approximation to the maximum mean migration rate they can sustain, although it might be slower on long time scales in practise due to the need to nest for litters etc.