This is the most common "not exploitable" CVE I have to deal with at work all the time. Things like buffer overruns when passing headers, but my server shouldn't be accessible to the public Internet anyway, and if it is, then we have much bigger problems. So yes it's technically exploitable IF other safeguards fail, but the reason it's irrelevant is that if those other safeguards fail, we are in deep shit anyway.
It's been proven over and over and over and over and over and over and over and over and over and over and over ......
that requiring access to a privileged network is NOT a sufficient security boundary! Someone you don't like always somehow ends up getting access to the network.
But if you have proper risk-based vulnerability management, you should already have classified that CVE as a lesser priority. This is something that modern LLMs should in theory make a lot easier, although I’m unsure if workflows exist to continuously build a proper architectural understanding of your systems, at least at a feasible cost.
This sounds like a piss poor implementation of zero trust on your part.
Security is an onion, you have lots of layers because layers peel off and fail all the time. With your current setup a single foothold gives an attacker all the lateral movement they need for full exploitation of every single thing you own blowing past the other layers.
Or you can just fix the issue that way if IT screws up you are not vulnerable. Or maybe next year you will decide it is useful to connect to the internet.