i read that something like 1/3 of all human caused extinctions are because we keep bringing cats with us

Do you have a source for that? Intuitively 1/3 of all species extinctions (keep in mind this in general includes plants and other kingdoms of life, not just animals) sounds far too high imo. Maybe you have read that number in a slightly different context, like bird deaths in urban areas, or perhaps in a more specific context similar to the one in your link? Don't get me wrong, like your link shows, (house) cats can easily have a devastating effect on the local wildlife, in particular birds and small mammals or reptiles (wikipedia has an article on the topic, although I didn't find anything like your numbers in it). But as far as I know the major ways in which humans have caused extinctions are historically overhunting (mostly affecting large birds and mammals), habitat loss in particular since the advent of agriculture, and more recently of course the effects of the climate crisis since the industrial revolution.

No, it says

100 to 1,000 times higher than the background extinction rate

both in the general intro and in the "Extinction rate" section, and

10 to 100 times higher than in any of the previous mass extinctions in the history of Earth

in the "Extinction rate" section (both verbatim quotes from its first sentence).