Your SIM is tracking your location

Whenever your phone is switched on with a SIM in it, the mobile network knows roughly where you are, all the time. The phone constantly checks in with the towers around it so calls and data can reach you, and each check-in tells the network which tower you are near. That location is recorded, and it is available to your carrier and, through them, to others.

An eSIM changes nothing here. It is a SIM built into the phone instead of a plastic card, so it behaves the same way. The only thing that stops the tracking is turning the radio off, which is what aeroplane mode does.

Your calls and text messages travel through the network in the clear as well. Your carrier can see who you call and text, when, and the contents of an ordinary SMS. All of that is logged.

Two partial fixes

Signal replaces your calls and messages. It sends them over the internet with end-to-end encryption, so the network cannot read them or see who you are talking to. Use it in place of normal calls and SMS.

Mullvad VPN encrypts your internet traffic, so your carrier and your home internet provider cannot see what you browse.

Both are partial. Signal fixes your calls and messages, and Mullvad fixes your browsing, and neither stops the location tracking. Your location still goes to the network for as long as the radio is on. Only aeroplane mode, or leaving the phone behind, stops that.