I suspect that there's no persuasive evidence that character traits are determined by genetic factors in ways that we can control or reliably predict.
A quick google found a twin study suggesting that they're significantly inheritable: https://pubmed.ncbi.nlm.nih.gov/8776880/
I guess mental illness can count as a personality trait, but I think there's considerable scope for personality traits well below the level of mental illness.
Neither of our anecdata will be useful for much here; I could just as well say that actually children usually resemble their parents less than you seem to think.
> There is probably plenty of research out there that tries to find out how much is due to nature or nurture.
Probably! But I don't know what it is, or what its conclusion is, so just saying that it probably exists doesn't advance either of our arguments.
https://www.nature.com/articles/s41380-018-0263-6
30-60% according to a bunch of studies. This particular study puts it closer to 60% than to 30%, which is in line with my own expectations but it's not a settled research question yet.