Try logging out of your account in the iTunes Store, then log back in with the account used to purchase the app. Then launch it already logged in, see if it will activate. If it does, you should be able to log out of that iTunes account, and then log back into your normal account.
CAVEAT: Backup your iPhone first in case anything goes sideways. I have to do this on my Mac with a couple of different accounts and it works fine, but I realize the the MacOS may handle it differently than the iPhone, so hard to know for sure if it will work.
Another option is to try family sharing from the account you used to purchase the app, and add your second account as a shared account.
It stil runs just fine on my iPhone 11 Pro, but it's on the original account used to download the app.
Good luck,
Tony