Help with startup skipping setup.

That is all the information that service can provide. Its trade-in value is just an estimate anyway, and you won't know how much you will actually receive until they make a final determination.

Refer to Apple Trade In - Apple. There is a lot of "fine print". If you are not certain about its specific configuration just take your best guess. The worst that will happen is that they revise the estimate, which you are free to accept or reject.

You can always reinstall macOS as described in What to do before you sell, give away, or trade in your Mac - Apple Support. Set up a temporary User Account to determine the information you desire, then erase the Mac and repeat those instructions. Seems like a lot of effort to go through though.

I understand you need to identify the specific model MBP so that you can estimate its trade-in value.

You can use this service: Check Your Service and Support Coverage - Apple Support.

Determine its serial number by clicking the link on that page. How to find your serial number, followed by Identify your MacBook Pro model - Apple Support:

• Find the serial number printed on the underside of your Mac, near the regulatory markings. 

It is laser engraved in very tiny text.

You have three options available:

1. Complete setup & check the information, then perform another clean install of macOS.
2. Install macOS to an external USB drive, boot from that external drive to get the information. This option provides the advantage that you only need to install macOS one time to an external drive and use it on multiple Macs to get the information needed (assuming the OS used is compatible with those other Macs).
3. Create & boot from a bootable Knoppix Linux USB stick. There should be an app (maybe apps) installed which will provide some details about the system including CPU, GPU, memory, and storage. There are definitely multiple ways to get this information.

Choose the option you feel most comfortable with.