Missing Add eSIM option in 13 pro max

There are two possibilities for your iPhone:

1) Your iPhone was not manufactured for use in the area in which you live

2) Your carrier does not support eSIM

Tap Settings > General > About

Now tap directly on the Model Number and a 5 character number will appear.

Example......A2484, A2643,A2644

What number do you have on your iPhone 13 Pro Max?

you’re currently in the community thread, we’ll try to help as good as we can, but I’ve included a link to official support down below.

how add an eSIM is explained right here: About eSIM on iPhone - Apple Support

Attention: if your iPhone has been purchased with a specific mobile [data] plan, it might be “carrier-locked”, means that you potentially can’t add an eSIM or generally insert any SIM card from another provider.

Also: if your iPhone 13 model was manufactured for China, Macao or HongKong markets, it doesn't support eSIMs, just 2 physical SIM cards.

Please contact Apple support directly here if you require further assistance: Contact - Official Apple Support

eSIM is not supported in Hong Kong and China mainland, so your phone cannot use eSIM.

So, iPhone manufactured for mainland china, unfortunately does not support eSIM technology. Sorry for your inconvenience.