I FINALLY found a solution after searching online and clicking around on my Macbook Pro. So prior to upgrading to Catalina, I had music on both my iPad and Macbook. After I upgraded, I bought some music on my iPad not realizing that it wouldn't sync over. Let me tell you, I am so frustrated about all of this.
To get music purchased from your iPad (and I'm assuming iPhone) to sync over to Macbook Pro, I went into the Music app, then navigated to iTunes. In iTunes, I went to "purchased" in the righthand column. I toggled over to "not in my library" and saw all of the music I purchased on my iPad. They all had the cloud symbol on them. I clicked and downloaded them all and now they are in my library on my Macbook! *phew*
I'm not sure if this would work in reverse from the Macbook to mobile devices, but it may be worth a shot rather than trying to plug things in and doing it manually, or paying for a subscription. I'm sorry, but after spending thousands of dollars on my Macbook Pro and iPad, I refuse to pay for an additional monthly subscription for music that I paid for. It's ridiculous.