If you are manually connecting to the NVR then yes, you need a static IP or there is no way to find it.
If you are using the P2P service in the app or PC software and scanned the barcode, you may not actually need to have a static IP set.
I ALWAYS set a static IP and reservation in the router, even if it doesn't actually need it. It just makes troubleshooting easier.

IP address = 172.16.x.x thru 172.32.x.x are private IP address (same as 192.168.x.x or 10.x.x.x addresses). So it depends on what the full network ID of that 172.x.x.x IP address is, will determine if its a private or a public IP address.

The only time you should get a public IP address, is if you are plugged directly into a modem only! Or if someone has DMZ'd the port your device is on.

Is this a 4G modem the NVR is plugged into? Make & model would help determine what is going on.

I actually have a brand new LTS LTN8708Q-P8N NVR sitting in my van right now. With (4) LTCMIP3342W cameras. Customer has LTS systems at his businesses and wanting to put a system at his home that works exactly the same way. Will be installing it next week but was going to pre-configure on the test bench this weekend and get all the firmware up to date.