Apparently there's research. I did a search, low and behold this is known.

kyberias · on Feb 22, 2019

There is no credible evidence that antibiotics "cause schizophrenia". On the contrary, there are trials to use antibiotics to treat it.

macawfish · on Feb 22, 2019

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2745871/

Here's a case of Levofloxacin inducing acute psychosis. For someone at risk of developing chronic psychosis, acute psychosis can trigger an avalanche.

There are other cases in which this has happened, and it's to the point where the FDA has administered a warning:

https://www.fda.gov/downloads/Drugs/DrugSafety/UCM513019.pdf

Schizotypal disorders are dynamic and non-deterministic. So I agree with your skepticism around the word "cause". But in this case, I think it would be unwise for someone with a history of schizotypal symptoms to use fluoroquinolones.