App Store requesting old Apple account for app updates

Recently went to update a couple of apps (the main one for me was Spotify) but the App Store is suddenly asking for login info for an old Apple account (one I haven’t used for around 10 years, which my parents set up and still use).

These apps were previously updated fairly recently using my account, but now it’s like the account linked with them has changed.

Is there any way I can sort this out, without having to delete the apps and potentially lose the data and logins associated with them?

[Re-Titled by Moderator]