Thanks for reporting this in! In the future, please add this to the stickied Bug Report thread rather than as an individual thread so we can keep ongoing track of the status of different known bugs in one place. We've replicated the issue on our end for both MV and MZ Demo Projects. It seems the IsiahCGCPartyUI_A plugin is at least one of the culprits.
With IsiahCGCPartyUI_A at 1280 x 720: Unable to pick Cards in my Hand, but still able to interact with the Buttons.
Without IsiahCGCPartyUI_A at 1280 x 720: Able to pick Cards in my Hand and also do other Touch interactions.
We can issue a fix for the Party UI plugin at the next minor patch (v1.3.5) that would re-enable Touch input for the Hand, until then we would recommend turning OFF the Party UI plugin if you are using a higher resolution than the default 816 x 624 px. All Party Battle functions should still work with just the Core Plugin, they will just look a little less presentable.
Please let us know if the issue is resolved on your side or if it continues to persist. We can continue to troubleshoot until we have found a fix that works for you :)