The file-sharing software allows for copying ("syncing") all or part of an iTunes library to an iPad, space permitting. Then, when it's on the iPad, it's portable - I can carry it around and play music directly from the iPad. I can either listen through the built-in audio jack (on my older iPads), or I can connect to the USB outlet on newer ones. I use the USB outlets, and I put a DAC (I use dragonquest cobalt DAC) between the adapter and headphones. The sound quality is pretty good. Regarding using the iPad as a remote means of playing from the iMac, the whole point of loading music onto the iPad is that it's portable, and I don't have to be playing it from the libraries on my iMac. I should say, I haven't spent a lot of time trying to run anything remotely from the iMac. File sharing has never worked for me - loading takes forever, and then the system always, always either crashes or freezes.
I have several iPads. And I have several libraries on my iPad, totaling 1.6-1.7 Tb. I load different libraries to different iPads.
The question I raised in my first message was about the syncing process, which really is a bit sketchy.
regarding the query about Apple Music - all my music is ripped from CDs. I don't think I have a single track downloaded from Apple music or the Apple store.
I have several iPads - new and old. My iMac was purchased in August 2019. I'm using the Mojave OS. My wifi is slow I guess - 15TB download.