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