Add eSIM option is missing on my iPhone 13 Pro

That iPhone model should support eSim. If you are not seeing it, your carrier hasn't provisioned your account for eSim OR they don't support eSim. Either way, you need to contact your carrier for help. This isn't an Apple issue.

If this follows the usual pattern, you have a dual-SIM iPhone 13 pro Max model number A2644, and those don’t have eSIM.

To confirm…

What is shown in settings for the Apple “A” model code?

Settings > General > About > tap on the Model Number “M” code shown, and the “A” number should appear.

If this iPhone 13 Pro Max is the usual no-EID report around here, it’s a grey-market purchased dual-SIM iPhone model originally sold in China mainland, Hong Kong, or Macao, and this iPhone will show the model code of A2644.

No dual-SIM models have eSIM, so no EID will be shown.

And no, eSIM cannot be enabled and eSIM hardware cannot be added.

Identify your iPhone model - Apple Support (lists the “A” codes for most (all?) iPhone models, and where each was sold.

If this iPhone “A” model is not one originally sold in China mainland, Hong Kong, or Macao (and thus without eSIM, and thus without EID), contact your carrier first, and then contact Apple Support.

Masiam wrote:

What exactly is carrier and how can I contact them?

Your cellular carrier, mobile phone provider, etc.

Masiam wrote:

What exactly is carrier and how can I contact them?

Whoever you pay for cellular service is your carrier. You pay them, likely once a month for service.