If you want to have a working phone, you need google apps (Google Maps, Google Play Services (used for many apps' notifications, location, analytics, etc.), Google Play Store, YouTube app). The Open Gapps project packages these nicely for use with LineageOS, but installation is janky (download a .zip file, install it using TWRP). note: despite being called "open", Open Gapps are proprietary, but packaged using open source software. Using LineageOS in this way is the sane/easy default that most LineageOS users probably choose. Using this method, you must sign in to google play services to install or update apps through the play store. Google play services includes a google analytics api, a a device registration program that generates an advertising id (so does iOS), Google also collects location data associating Wi-Fi hotspot with GPS coordinates (so does iOS). I'm not sure of the full extent of what info google collects, but it is probably substantial, and most probably happens through google play services. You could dodge this tracking by not logging in to Google Play Services and using a play store replacement like Aurora Store or Yalp (play backwards).

Another option is to use microG, a derivative of LineageOS that re implements parts of google play services with open source and throws out the rest. YMMV, but I have used it and my phone worked, excepting some apps' notifications because they use google cloud messaging. I never signed in anywhere with a google account, but I did have google maps installed (I haven't found a good replacement on Android). Google probably got rather little info from me, but they did get my location sometimes.