That's not a standard Windows prompt, looks like some third-party application is intercepting the call.
Check the registry: HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows NT\CurrentVersion\Image File Execution Options - for a key named taskmgr.exe. If it exists, see if the taskmgr.exe key has a value called Debugger. If so, delete the Debugger value, or rename the taskmgr.exe key to e.g. taskmgr.exe.old.
Then try launching Task Manager again.
If there's nothing in the registry, you could monitor the process tree in Process Explorer and watch what happens when you execute taskmgr.exe. You could also use Process Monitor if you want to dig deeper and find out exactly what's happening - you can filter out Microsoft processes to make it easier to see all thirdparty software interactions.
I’ve never really understood this approach. If my work laptop prevents me from doing work, I open a ticket, cc my boss, and move on with my life. I’ve got enough other stuff to do and why take on the risk associated with circumventing company security controls just to get that TPS report in on time? I’ve got documentation showing that I tried and couldn’t complete the work because of the security control.
This is the right way to do it. Make it clear this IT process is causing reduced performance. Especially if you're a profit centre you will likely see the problem solved soon enough.
This specific thing. A password on task manager is really dumb though. I assume they have some spyware they don't want users to be able to stop. But, most of this kind of software (think antivirus) generally have other ways to prevent tasks being closed. They don't need to remove task manager. Task manager is an important and needed tool for any windows user.
Anyway, it looks suspicious. Resolution of that window is not quite right, it's fuzzy. Though I now see you said the .exe is signed, so I guess it's just some scaling bug.