You can use the same .mp3/.m4a (AAC or ALAC)/.m4p/.aif/.aiff/.wav etc. files in the Apple Music app on newer systems without the iTunes application. Apple Music user guide for Mac - Apple Support
When migrating, the migration software will copy and convert the library as needed; the media files themselves will be re-linked (and moved if applicable) but untouched. Transfer to a new Mac with Migration Assistant - Apple Support
For manually adding the old music files to the Music app, you may use drag-and-drop of individual files or group of files, with the Library open. You may group into playlists (like albums) before or after adding the files to the Library.