RESOLVED Per Intel documentation here Intel® AMT SDK Implementation and Reference Guide Starting from Alder Lake platforms with Raptor Lake CPUs running Intel CSME 16.1 firmware, remote connections to Intel AMT unsecure TCP/IP ports 16992, 16994 and 623 are no longer supported. TLS ports 16993, 16995 and 664 must be used for connecting to Intel AMT. Starting from Intel CSME 19 firmware on Arrow Lake platforms, connecting to Intel AMT without TLS is not supported at all (i.e., also local connections must use TLS ports). I hadn't noted the ME firmware version before upgrading but it must have been pre-16.1. This computer has an i7-12700 (Alder Lake) so it's a simple matter of the port I was previously using is no longer available.  
As one of the first tasks after powering on this new Precision 3460 I used the MEBx interface to configure Intel AMT/vPro. After configuring and enabling the network settings, I was able to connect to the vPro interface via web browser at the IP address I configured, for example [URL] I also use Intel Manageability Commander so I added it to that tool and was able to connect. In other works vPro was working as expected. I then did firmware/driver updates, in this case using the Dell Command-Update utility. I'm not 100% sure if was immediately after those updates, but at some point vPro stopped responding. When I try to connect via web browser there is no response. A Wireshark trace confirms that no packets are being returned. Same result with Intel Manageability Commander. vPro is no longer responding on port 16992. I've since tried manually downgrading the BIOS but no luck. I took it from 2.5.1 (latest) to 2.4.0 and then to 2.1.0. I *think* the only way to downgrade the Intel Management Engine Firmware is via the BIOS updater on Dell devices. From what I can gather, all BIOS installers for this device newer than v1.8.0 contain Intel Management Engine Firmware v16.1.25.2128, which is currently installed. BIOS updater 1.8.0 contains Intel Management Engine Firmware v16.1.25.1932. I'd be curious to see if downgrading to that version fixes the issue however that's not possible as there is a note on the newer BIOS updaters stating "Once the BIOS is upgraded to version 2.0.0 or later, you cannot downgrade the BIOS to version 1.8.0 or earlier versions." Looking for any other suggestions to troubleshoot this issue.  
Precision 3460 - Intel AMT/vPro not responding