Few years back, I bought an app with my previous email address - job related one.
If you no longer work for that company, that company has already deleted your work email address. This is done as soon as you have left the company so that you can no longer log in. You no longer have any rights there.
An deleted email address, it is no longer valid, it simply no longer exists and it no longer works.
You may not be able to change that email work address because it is no longer exists.
Your Apple ID is the personal account you use with all Apple products and services. It includes the email address and password you use to sign in, as well as the contact, payment, and security details that you use with Apple.
You can’t merge multiple Apple ID accounts.
See -> Sign in with your Apple ID -> Sign in with your Apple ID - Apple Support
The app was paid once, when initially bought it.
If you want that app now, you'll need to purchase it again with your private current Apple ID.