that's really it. Lots of apps find lots of ways to call home, and Google, especially, is constantly calling home from Android, so unless you're going to, like... uninstall all but one Google app to test it in a vacuum, and then add other apps one at a time, it's not going to work. Also, that experiment won't work, because we already know that Google Play Services handles most of these shenanigans.
the technology my device uses to communicate with services, including self-hosted services, is known as the internet. local area networks only work in the local area, which frustrates the purpose of a mobile phone—being mobile, and all.
both the server and the client must be connected to the internet to communicate with one another across significant distances.
You can block a service from establishing outbound connections while allowing it to respond to inbound connections. It's pretty common to do this because server software generally has no business calling out unprompted.