I'm trying to do Home Sharing in Mojave but "Media Sharing" does not show up in System Preferences > Sharing (see below). Any suggestions?

Thanks for your replies, turingtest2 and JayanthSahasranamamula. At first the "Sync your iPad" solution looked like it wasn't going to work, because my iPad did not appear as a device in iTunes when I plugged the iPad into my MacBook. iTunes warned me that I needed to update my software to get my iPad to appear.

That error message gave me the impression I would have to update both my iPad and my Mac to their latest OS versions to get the iPad to appear as a device. Since I have the final version of iTunes for MacOS (12.9.5.5), I am unwilling to update my MacOS past Mojave. However, to my pleasant surprise, it was adequate to update my iPad to the latest version of iPadOS (15.2) to have the device appear in iTunes. After that, it was easy to sync my iPad to my iTunes library.

Note that I have "Home Sharing" turned on in iTunes.

yes, Home Sharing is enabled, but that's not sufficient to enable copying my iTunes library (including playlists) to my iPad. That is my ultimate goal.