The association/correlation may be very real.
However, this does not mean that having cats increases risk of schizophrenia. It can mean that people with a heightened risk of schizophrenia are more likely to have cats.
Correlation is not causation, but it does sometimes mean that there is a link that should be investigated.
This was a retroactive analysis of previous studies, not an original study. This means that it is fairly low on the scale of scientific robustness. I would always take such retroactive analysis with a huge grain of salt.
Plus the study includes “schizoaffective disorders”...the schizophrenia designation came after mathematically hacking, chopping, and filtering the data from all of those low power studies you aptly pointed out.
If they are sure of their conclusion, they themselves should design a high powered prospective survey to prove it, and pay with their own funds or funds from people who volunteer the money.