How to remove inactive eSIM entries if "Update Contacts" option doesn't show up?

1. Is this your corporate iPhone? Then please contact the system administrator of your corporate
2. If it is your personal device, in that case, do you have any profile installed by your corporate/organisation/enterprise/School Management?
   1. Erase the profile added by you If you have installed a profile on your own --> Install or remove configuration profiles on iPhone - Apple ...
   2. Or please contact the system administrator of the organisation who provided the profile to you
3. To remove network settings installed by MDM, go to Settings > General > Profiles & Device Management, select the management, then tap Remove Management. This also removes other settings and certificates provided by MDM. See “Mobile device management (MDM)” in the iOS Deployment Reference.

Does your phone use an eSIM or a physical SIM card?

1. For eSIM users: You can remove the data plan from your device without needing to contact your carrier first. Here's how:
   1. Go to your phone's settings (the exact steps may vary depending on your phone model and operating system).
   2. Look for a section related to "Cellular" or "Mobile Data."
   3. Find the data plan associated with your eSIM and select it.
   4. You should see an option to "Remove Cellular Plan" or "Delete eSIM." Choose the appropriate option.
2. For physical SIM card users: You'll need to take two steps:
   1. Remove the physical SIM card: Locate the SIM card tray on your phone and carefully eject it. The SIM card itself will be a small chip inside the tray.
   2. Contact your carrier to cancel your data plan: Removing the SIM card from your device doesn't automatically cancel your service. You'll need to contact your carrier to officially discontinue your data plan and avoid any unnecessary charges.

Important points to remember:

• Removing the data plan from your device (eSIM or physical SIM) does not cancel your service with your carrier.
• To completely stop service and avoid charges, you must contact your carrier to officially cancel your data plan.

By following these steps, you can effectively remove your data plan, whether you're using an eSIM or a physical SIM card.

For better clarity watch the GIF below

The "Update Contacts" option you're seeing in the context of inactive eSIMs on iPhone 13 likely isn't related to your address book contacts. It's more specific to the cellular plan information associated with the eSIM.

Can you pelase provide the Apple Article that you are referring to?

Unlike some Android devices, contacts are neither stored locally on an iPhone nor in SIM/eSIM. They are synced to an email account that you have Google, iCloud, AOL, Exchange, Outlook, Yahoo or any Other