Does Galileo track my phone?

Your phone determines its position by combining signals broadcast by navigation satellites (Galileo or others), which only transmit the signal to your phone and your phone is not designed to send back to these navigation satellites any information computed by your phone, such as your position hence Galileo does not track your device.

However, apps on your phone like ridesharing or mapping services and many others of various nature may share your location with application providers via the internet.

Only emergency beacons can send location data to Galileo satellites (purposefully).