Is the main site account of an Add-On Domain visible in any way? For example, my site: https://bonafidebankruptcy.com/ is an Add-On Domain, but I don't want random people to know that. Do I need to get a different level of hosting or do anything else to keep it separate?
Are we talking a whois type of privacy or something else as in: https://whois.domaintools.com/bonafidebankruptcy.com ?
All of that info is fine to be public. What I'm concerned about is the site being identified or associated with my siteground account site, which is a music-related site. I don't want them to be publicly connected.
A DNS Lookup would show them on the same IP Address. If you changed your Addon domain to a separate cPanel account then you could have a dedicated IP assigned to it to help further separate it. But, other than that an addon domain appears as separate as any other account on a shared host. It's essentially just another VHost entry, and the document root it's pointing to wouldn't be publicly available.