7060 MT, i5-8500 support vPro and AMT?

Only if you are not from an Embargo'd country.  AMT is an option its not globally standard.

https://www.dell.com/support/article/us/en/04/sln143077/manufacturing-management-mode-settings-guide-intel-amt-on-dell-systems?lang=en

A label in the cover indicates which features ARE or ARE NOT there.

AMT Label

https://www.dell.com/en-us/work/shop/desktop-and-all-in-one-pcs/optiplex-7060-tower-and-small-form-factor/spd/optiplex-7060-desktop

Identifying vPro Enabled Systems
Intel vPro Technology has been around for generations.
– Ivy Bridge CPU supporting Intel VT and TXT Remote KVM (Keyboard/Video/Mouse)
Intel technology to enable the remote IT admin to see and control a system even outside the OS or driver environment

Out of Band Management of Dell Business Client Systems using Intel vPro

–Panther Point Digital Office PCH (Q77/QM77/QS77)
–TPM 1.2, Revision 103 (or better); possible update to 116 pending
–BIOS that... Enables: Intel VT-x, VT-d, TPM 1.2, AMT; and Supports: TXT
– Intel ME firmware 8.0 (or better)
– Lewisville Gigabit LAN (82579LM)
– Intel WiFi Link (Puma/Jackson/Kilmer/Taylor Peak)
– NB only (DT optional)
– Successful pass of Intel’s Brand Verification Tool (BVT) or Technology Verification Tool (TVT Fixed workstations only)
Provisioning a System for Out of Band Management

And by the way, this one way selection is reversible. https://imgur.com/a/Mh9Jz