You can save just about anything that a procedure creates using ODS OUTPUT. See
https://blogs.sas.com/content/iml/2017/01/09/ods-output-any-statistic.html
and
https://stats.idre.ucla.edu/sas/faq/how-can-i-use-the-sas-output-delivery-system/
For example, you can save the lsmeans to a dataset
ods output lsmeans= my_lsmeans;
lsmeans bact*sick / plots=meanplot(join cl sliceby=bact) ilink cl;
and then export that dataset to CSV or Excel.
I do not recommend using a Type I error adjustment on all pairwise comparisons of interaction means. As you note, when you have 25 means, there are 300 possible pairwise comparisons, many of which you are not interested in because they compare something like B1S1 to B3S4; slices make comparisons for one factor within a given level of another factor so you don't get those "cross-level" comparisons. At most you may be interested in 100 of the 300, but still, if you invoke Type I error adjustment for 100 comparisons, most, if not all, of the p-values will be close to 1. Granted, you won't make any Type I errors, but you won't have any power (i.e., you'll potentially make a lot of Type II errors).
I don't find pairwise comparisons to be very helpful in deciphering interactions because an interaction is a comparison of (pairwise) comparisons. Instead, I estimate a carefully chosen set of contrasts that are meaningful in the context of the study. I might group those contrasts into sensible "families" and control the family-wise Type I error separately for each family. This task, including the multiplicity adjustment!, can be accomplished using the LSMESTIMATE statement; see
https://support.sas.com/resources/papers/proceedings11/351-2011.pdf
The Bonferroni adjustment is excessively conservative (i.e., you lose too much power); I generally use the simulate method and I always specify the random seed for reproducible results. If you need to control Type I error for multiple tests, the goal is to do so while maintaining as much power as possible; not all methods are equally good (and some are quite lousy; some don't even control Type I error appropriately).
I may be able to look at your results within a few days.
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