Different emails at App Store and Apple ID

You can't change the App Store email to become equal to Apple ID email. That would be merging Apple IDs and Apple IDs can't be merged. I suggest you update the email for the App Store ID to get a current email address as a first step. Note the restrictions in the article.

Apple ID Name Change.        

 What to do after you change your Apple ID or password - Apple Support    I suggest doing this before you change your Apple ID or password.

You can then continue to use the App Store ID in the App Store/iTunes or you can sign out, use the Apple ID, and you can try setting up Family Sharing between the IDs if you want to be able to share purchases made with the IDs.

Family Sharing.         

Family Sharing - Set up.       

My main Apple ID and my App Store/iTunes ID are 2 different Apple IDs and so far, that hasn't caused any problems.

This may be your problem. What to do when the Mac App Store shows a different Apple ID for software updates https://www.macworld.com/article/3267709/mac-app-store-apple-id.html. This document refers to a prior owner, but is also applies to cases where a current owner's old Apple ID is the problem.

Basically, If an app is purchased/downloaded using one Apple ID, then you can't update it with another Apple ID. The app is inextricably linked to the first Apple ID. You'll have to delete it and repurchase/download it again with the second Apple ID.