Hello!
As far as I know, an internet connection is required for activation, which means that a connection to a remote server will be made on behalf of my IP address.

  1. What server is phone connecting to (eSim activation)? With the mobile operator's server?
  2. Through which connection is the connection made? Through VPN or does it bypass VPN and use direct connection (WiFi or Cellular)?
  3. What data is sent to the remote server?
  4. Will there be more connections to the remote eSim server after installing the SIM card or is it a one-time connection (only for activation)?
  5. If I activate eSim before installing GrapheneOS, can I then remove or replace eSim already in GrapheneOS?
  6. If the eSim card is activated before installing GrapheneOS, then when working in GrapheneOS there will be no reconnections to the remote server?
  7. Is it possible to use a physical simcard (active status) and eSim (active status) at the same time? For example, use the Internet from a physical SIM card, and use eSim to call and receive SMS. That is, will both sim cards be active on the network and call access or do they need to be switched?

My main task is to prevent the IP address of the VPN server from which I access the net from leaking and to understand when and to which servers the connection for eSim activation (or not only activations).

Thank you.

To abbreviate things, I will not itemize my response as some of what you're asking is redundant.

An eSim is a 'programmable' sim that is already part of your hardware. The activation process of the eSim will vary from carrier to carrier. You need to provide them some information such as IMEI & IMSI once generated locally on your phone.

During the registration process you will 'log' an IP address with the cellular carrier, but the eSim you create on your device will communicate with a cell tower near by. That will be logged by the cell tower but that is how cellular communications work. Ultimately that eSim will be tied to a phone number and whatever other information you provide to the cellular service provider since they need to link your IMEI and IMSI with a phone number. They will also have your payment details any anything else provided. (email password etc)

The portability of your eSim will also vary depending on the carrier you choose. It's something that you will need to manage if you change devices or wipe your OS. Know what you need and test your process before you make a big move.

You can use a real sim and eSim simultaneously in a sense but you can only use one at any time even if both activated on your device. But toggling on/off is easy with GrapheneOS.

In the end, what you provide will be logged in some sense by a cellular service provider or a cell tower you interact with. Again this is how cellular stuff works. GOS helps by not allowing apps to access these identifiers.

https://grapheneos.org/faq#hardware-identifiers