What happens if I do a restore or change phones with an eSIM?

I have just came from an Apple store having just have my iPhone XS Max replaced due to a fault from factory. I also had an E-SIM and basically if you are restoring your device the E-SIM will not be affected, just like your physical SIM.

New devices however like in my situation, you will need to go to your carrier and request a new E-SIM QR code for the number you had on the previous device.

Only took 5 mins with EE, just make sure to have photo ID and knowing this information will make it a whole lot easier if you are expecting to have a device replaced.

i have an iPhone XS with an AT&T eSIM. In order to troubleshoot a 3rd party SIM for CDMA access, I recently attempted to reset cellular accounts through all available options; reset network settings, remove all cellular plans, erase all content. Some attempts to restore my AT&T eSIM required scanning the eSIM barcode so hold on to that. After the complete erase, however, the eSIM oddly remained and didn’t require the barcode to re-activate the account.

I've been having the same question too. I ensured myself that, technically, the eSIM stored its data on a small piece of the circuit, separated from iphone main storage. So restoring the phone shouldn't have effect on eSIM.
After restoring the new phone, the one with eSIM, with the previous backup from iTunes. eSIM still there.

To answer your question, Restore phone wouldn't have effect on eSIM but I'm not sure that erase content and all settings option would erase eSIM or not.