LineageOS does not come with Google Play services, so it's a lot quieter. It should also be possible to find all instances of outbound requests in its source.

That being said, I ran tcpdump on my router for about 10 minutes with no background applications and didn't observe any traffic. There's a (weekly? forgot the default) update check that's enabled by default, everything else is disabled.

When connecting to a network, HTTP and HTTPS requests are sent to Google-owned domains for the captive portal check; you can configure a custom URL instead: https://gist.github.com/edwardw/cb99236a592900c4f26fb0d8f474....