How to select the level of confidence when using confidence intervals? Saw the expression of "95% confidence interval is commonly used" in a lot of literature. I want to understand more about why 95% (or 99%) is a good level to use. Or is there a general methodology to determine what a good level to use is?
Commonly see the need for bootstrap confidence intervals from data with unknown (non-Gaussian) distributions. For various kinds of metrics (e.g. median, rank, specially customized measure). Is 95% a good starting point for all sorts of metrics? For some use cases, a more stringent 99.9999% confidence interval is agreed by the field. In other instances, people use a more relaxed level. I hope to get an understanding of the general theory or methodology to determine when to use what level.

Richard McElreath puts it nicely in Chapter 3 of Statistical Rethinking, second edition:

Rethinking: Why 95%? ... This customary interval
also reflects the customary threshold for statistical significance,
which is 5% or p < 0.05. It is not easy to defend the choice of 95%
(5%), outside of pleas to convention. Ronald Fisher is sometimes
blamed for this choice, but his widely cited 1925 invocation of it was
not enthusiastic:
“The [number of standard deviations] for which $P=0.05$, or 1 in 20,
is 1.96 or nearly 2; it is convenient to take this point as a limit in
judging whether a deviation is to be considered significant or not.”
Most people don’t think of convenience as a serious criterion. Later
in his career, Fisher actively advised against always using the same
threshold for significance.
So what are you supposed to do then? ... For example, why not present
67%, 89%, and 97% intervals, along with the median? Why these values?
No reason. They are prime numbers, which makes them easy to remember.

