>3. Check for instructions on your previous iPhone to confirm the transfer. To confirm, tap Transfer or, if asked for a verification code, enter the code that's displayed on your new iPhone.
You're looking at the section titled “Use eSIM Quick Transfer on iPhone”, which explicitly states “Some carriers support SIM transfers from your previous iPhone to your new iPhone without needing to contact them.”
So this doesn't apply in the case where you contact the carrier to transfer the eSIM. Which you'd have to do if your SIM card were damaged or lost anyway…
1) Your smartphone fell and the screen broke (or some other problem).
2) You have another smartphone (an old one or a spare).
In this case the phone is broken but the SIM is just fine.
With the old physical SIM you take it out of the old phone and you put it in the spare phone (no need whatsoever to contact anyone, not the phone manufacturer, nor your ISP, nor any website), both the old phone and the spare one can be any phone model (as long as they both use the same format of physical SIM).
With the new eSIM there is a procedure that needs that BOTH the old phone and new phone are working AND/OR you need to contact the ISP, the phone manufacturer or anyway you need to have an internet connection, additionally it seems that for some easier procedure both phones need to be running iOS 16 or above or however be connectable to iCloud.
This is more complex, and in some cases (connection to internet not available because you are alone in the woods or whatever and don't have a third device) impossible.
BTW this is not "my" information, is what I could find on the official support page of the manufacturer, maybe it is inaccurate or I am failing to understand what it says.
https://support.apple.com/en-us/HT212780
>3. Check for instructions on your previous iPhone to confirm the transfer. To confirm, tap Transfer or, if asked for a verification code, enter the code that's displayed on your new iPhone.