How to recover paid music from iTunes after changing iPhone model?

Re: "..... iTunes and music app ..." : " ... recover lost songs ..."

Apple Support’s online article:

About purchasing movies, TV shows, music, books, and ringtones from Apple - Apple Support

Eg: says:

“Any digital media you buy from Apple can be permanently downloaded on to an iPhone, iPad, Mac, or Windows PC.”

and

“Once downloaded, you can access content without an internet connection, and Apple can’t remove it from your device

Also:

Learn how to redownload your purchased content on an iPhone, iPad, Mac, or Windows PC:

Eg: Redownload music from the iTunes Store on your iPhone or iPad - Apple Support

Store availability and features might vary by country or region. "

Availability of Apple Media Services - Apple Support

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If you need to troubleshoot: You can see what to do, in the linked article below:

If there’s an issue when you redownload apps, movies, or other content from Apple - Apple Support