There is no "formula" for bootstrap confidence intervals; rather there is an algorithm which relies on iteration (and usually requires computer programming to achieve, as at least in PROC PLS, there is no bootstrapping built in). See https://blogs.sas.com/content/iml/tag/bootstrap-and-resampling
I am not aware of articles that compute standard errors or confidence intervals for PLS Models. In fact, almost every usage of PLS I have seen published ignores this entirely; if the model cross-validation says that the entire model is statistically significant, then the rest of the questions you ask are essentially ignored. PLS was developed outside the statistical community, and now that the statistical community has begun using PLS, they ask these questions, but I don't think there are answers, other than bootstrap and similar methods.
In the special case of Logistic PLS, where the algorithm actually fits many univariate logistic regressions, you can get the chi-squared test result (p-value and/or confidence interval) for each coefficient in the loading vectors; and also for the overall regression coefficient.
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