Hello Echelon,
I understand you have two Apple IDs. Merging is not possible and transfer is at best tricky and incomplete. Since apps are permanently tied to an account you may instead wish to share the iCloud contents of the other account to the app account and just continue with that one account. As far as I know there is nothing that is stored in iCloud that cannot be transferred or shared to another account with a bit of work. Read the links below for things you may need to do to transfer as much as is possible.
Apr. 2018 post by ASC helper Winston Churchill on transferring data from one Apple ID to another. Can I merge two iCloud accounts - Apple Community
Feb. 2021 tips from Eric Root Apple ID - Apple Community
Look into using Family Sharing to continue to be able to use items purchased with one Apple ID with other Apple IDs.
Family Sharing - What is Family Sharing? - Apple Support
Set up Family Sharing - Set up Family Sharing - Apple Support
Share folders with iCloud Drive --> Share files and folders in iCloud Drive on iCloud.com - Apple Support
Read How to use Shared Albums in Photos on your iPhone, iPad, and Mac - Apple Support about about how to share photos.
If you have signed into the ID on two devices then fortunately when you sign out of one ID and sign in with a different one it asks you in most cases if you wish to retain the data from it on your device. Say yes and then delete individual items you do not want.
Sign out of iCloud on your iPhone, iPad, iPod touch, Apple TV, or Mac --> Sign out of iCloud on your iPhone, iPad, iPod touch, Apple TV, or Mac - Apple Support
If another Apple ID is signed in you may need to enter the password for that ID to sign out of that ID first.
Click on this link to learn how to 'Sign in with your Apple ID' --> Sign in with your Apple ID - Apple Support