If you're planning to monetize it then you'll probably need to host it on your own anyway, so I guess you'll have to use a server. You can still make the base code open-source I guess, and add new features that are only available on your customized service. They are not mutually exclusive. There are dozens of open-source software out there that keep being updated and people support the dev through Patreon for example. Not sure how it would work on your project though, since the market is quite niche.