Using iTunes Remote on iPhone 11 to listen to purchased iTunes Music Currently on PC

I have synced my iPhone with my PC using a USB cable. I have turned on Home Sharing and my computer, using Windows 10, shows my purchased iTunes music synced, but nothing is showing on the iTunes Remote app installed on my iPhone 11. I am given the choice of selecting "Use Home Sharing" (which asks me to sign in, then takes me to a blank page with "Settings" at the top of the page) or the option to Connect Manually (I'm given a 4-digit code and directions for using Apple Music or Apple TV, which I do not use, or clicking the Remote button in the iTunes window--which I've done.)

I feel like I'm missing a step somewhere. Must I purchase the Apple Music app in order to listen to music already purchased through iTunes?

Your help is greatly appreciated.