iTunes versions: 11.4, 12.8.2 OS: Mavericks, High Sierra. Today I tried on a computer running Windows 7 and ITunes v220.127.116.11, it was able to turn on home sharing.You say iTunes 12 is affected too? What version specifically and on what macOS (iTunes 12.x.x is able to work with macOSes ranging from Lion to Mojave)?
Actually I forgot one step in the problem.As for Home Sharing I could turn it on and off all I want and so could I regarding iBooks on Mavericks where the iBook Store works perfectly (at least it did a few days ago). I believe iTunes Store and Home Sharing are using different connection routes. But I observe these drops since the rollout of Catalina.
There is nothing I see that says "Generate a verification code". Also I don't have an iPhone.To turn Home Sharing on fill out all the necessary login fields and append a verification code to your password. You can generate the code on your own by going to Preferences-->iCloud-->Security on your Mac running El Capitan and newer, or Settings-->Password & Security --> Generate a verification code on your iPhone (iOS 9& later or if you're running Yosemite and older).
iTunes 11 store on latest version of Mavericks opens, but I cannot click any items, so it's unusable.