What is the little key for…the one with my new iPhone 13 Pro Max?

If it looks like one of these:

it is a SIM removal tool.

As noted, it is the SIM card removal tool to remove the sim card from your phone.

what is the key for my new iPhone 13Pro (and how do I use it?)

I need a SIM # to port my phone number. Where do I find it?

Ok--I snapped in open, but there is no card inside. ??

You have to get a SIM card from your carrier with your phone number on it to insert into the SIM card slot. Or see if your carrier supports eSIM.