How to transfer downloaded music from old iPad to my new one?

Music and media cannot be directly transferred between devices. Any Music/Media content, transferred from your PC/Mac using iTunes (or Finder on later Mac computers) - or “Paid” material downloaded from Apples iTunes Service - must again be downloaded to your new iPad.

The reason for this intentional limitation, deliberately imposed by Apple, is to protect Copyright. In the case of iPadOS/iOS, Digital Rights Management (DRM) prevents direct copying of copyright material between devices is inhibited. This is intended to prevent the creation of illegal copies of potentially copyright material.

The iTunes Application on your PC/Mac maintains an authorised copy your media - whether this material is loaded from a CD, or downloaded from the Apple iTunes Service - and media derived from this library can be transferred to your iThings.

Music purchased directly from Apple's Music App (or earlier iTunes App, superseded by the Music App), can be dowloaded again directly to your iPad. The iPad User Guide describes how:

Add music to iPad and listen offline - Apple Support