Why can't I sync my personal music library from Mac to iPhone using the same Apple ID?

Why can’t I sync my personal music library the I created with all my old CDs from my Mac to my iPhone? I’m logged into the same Apple ID on both. I’m using OS Sequoia 15.3.1. When I go into the settings within my Music app on my Mac there isn’t the option to sync my library. I don’t feel like I should have to pay for an Apple Music subscription just to sync and listen to my own music. This is very frustrating.

[Re-Titled by Moderator]