Greetings. I cannot duplicate this problem after the update, with or without YEP_ItemCore. Although while troubleshooting it again, I found a display problem with the menu extension + extraparamformula that would've made the offhand crit and hit displays wrong.
I also have no issue with using only the menu extension to display pry and xpt.
Here's a poorly done image with mspaint to show various use-cases
The plugins are the exact same (except itemcore) as yours, in the same order, with the exception of BuffsStatesCore. In your load order, shield block should be immediately after BattleEngineCore, to prevent other plugins from interfering with the stuff it adds to the battle result, but I don't think that's causing this problem for you. Note that I don't think I ever really specified where in the load order to put ParryChance, but it should probably be above BuffsStatesCore as in my order above.
ExtraParamFormula is only using the default formulas for everything in it.
StatusCore has pry and xpt alone in the fourth column, and, as you can see, I don't have the exparamfix plugin at all.
The various snippets of the equip and parameters windows show that all four permutations of having two identical weapons equipped in various ways all correctly show the crit % for each hand as they are swapped around. The flail has +70% crit rate, and the actor has 4% base.
With ItemCore and independent weapons enabled, I was unable to duplicate this in the first place using the previous versions of the menu extension plugin. I checked again just now with itemcore turned on and got the same result as above.
I imagine, since your YEP plugin versions are about the same as mine are, that this project is quite old, it's possible there might be a problem with your core plugin files being out of date, messing with compatibility somehow.
I would suggest trying to reproduce this problem in a blank new project, with those plugins alone, and see if the problem still happens there. The last time someone reported weird problems like this with dual wield, it turned out their core files were woefully out of date, and updating them fixed the problem.
It's also possible that changes were made to some of your core plugin files, or some of the yanfly plugins you're using that are breaking compatibility with mine. Like I said, I'd start by making a fresh project, making Harold a dual wielder, and testing from there.