I just wanted to share my solution to this issue:
Changing power options for the device did not resolve the issue (disabled "allow windows to turn off to save power" and "energy efficient Ethernet", and we have all sleep modes disabled anyways)
Manually setting the connection type did not resolve the issue (Full duplex 1GBPS. It still worked with the settings set manually but the disconnects were just as common)
Updating to the newest drivers Dell had for our systems that hosted these NIC chips did not resolve the issue (tried, among others, 12.6.45.0, 12.2.45.0, and a 12.3 that I forgot to write down).
I spent two hours on the phone with an absolutely useless tech who in the end said she didn't know what to do. Escalating to a manager who assured me multiple times that an advanced tech would call me, but one never did... obviously did not fix the issue.
Installing third party NIC fixed it... obviously. Installing a PCI-e Intel card though did not. I tried different cables to different switches with no result.
The solution ended up in running the intel driver check utility which downloaded and installed driver set- 20.4.1 which after install shows as 12.15.30.0... quite a bit higher than the newest drivers dell listed for their workstations.
I am no longer purchasing the expensive and apparently useless Dell ProSupport for workstations. If they can't even help with this it in no way seems worth the money. Intel isn't free from blame here, its clear that MANY versions of their drivers have this issue and just pointing people back to their PC manufacturers for support is a cop-out. Yeah I get it, integrated components like these NICs probably make them next to nothing compared with CPU sales, but that sure sucks for us.
I hope this helps some others, troubleshooting this issue from the first profile corruptions it caused to pinpointing the network disconnects as the issue to tracking down a solution took months and plenty of false trails. I am deploying out the new driver set to all NIC cards, not just those with this issue, on my next patching day. I'll update if anything new gets stirred up as a result.