I can’t restore an app purchase after i changed the email address on my apple id

If you changed the email address and didn't create a new ID, have you tried signing out of the App Store/iTunes, restarting the device, and then signing back in?

Do the apps show in your purchases history?

Purchase History Review.  

It sounds like you created a new Apple ID. If so you have created an issue for yourself.

An App Store app is forever tied to the Apple ID used to acquire it (paid or free). The Apple ID is encoded into the licensed copy that is downloaded. It is in the copy's DNA. That is the only Apple ID that can redownload or update the app.

This would be the process to have followed to change the email address associated with your Apple ID;

Changing the email address you use for your Apple ID -

Change your Apple ID - Apple Support

If you have created a new Apple ID, your only option for reacquiring apps is to download them again with your new Apple ID. You will need to buy paid apps again.

M1 Mac mini, macOS 14.4.1;  Watch, series 7 GPS/cellular, watchOS 10.4; iPhone 12 Pro, iOS 17.4.1; TV 4th Gen, tvOS 17.4; HomePods, audioOS 17.4 and Airport Express w/ Airplay 2

Apps are free to update and to redownload when they are the same basic version with minor updates. But if this subscription version is a new and improved upgrade, then the developer can require that folks pay again to get the new version. The newest version is the only version that would be available in today's App Store.

Since you state that it was several years ago that you bought the app, this is likely a new version.

Not necessarily after the years that have passed and various new versions.

It likely shows in your purchase history that you can view in your account details through the App Store or the iTunes Store in the Music app.