I have LineageOS installed on my phone. Without the app InviZible Pro from F-Droid, my phone connects to Google servers for connectivity checks, system webview and time adjustments. The disadvantage in terms of privacy of /e/OS would be the default presence of micro g, which is proprietary. In LineageOS it’s not present by default.
Why don’t you use a decentralized VPN like NymVPN? It’s impossible for the company or anyone to take logs because your traffic is routed over several nodes. It’s like Tor but also adds noise to data and harder to deanonymize