Think of it like one-sided vs two-sided. You can have a 95% CI that overlaps with zero, like [-2, 30], because 2.5% of the probability mass is on >30 and 2.5% on <-2, but still the probability of >0 effect can be >95%. This can also happen with Frequentist CIs.
A credible interval is the Bayesian analog to a confidence interval.
Think of it like one-sided vs two-sided. You can have a 95% CI that overlaps with zero, like [-2, 30], because 2.5% of the probability mass is on >30 and 2.5% on <-2, but still the probability of >0 effect can be >95%. This can also happen with Frequentist CIs.
A credible interval is the Bayesian analog to a confidence interval.