This was driving me crazy. nRF Terminal extension in VS Code just silently fails. I was able to use the JLink Viewer app so I knew RTT was working correctly.
I then looked inside the source code for the extension, and as the title says, the extension is looking for JLink.exe in the wrong place* (*potentially the wrong place).
Note that while most users have program files [(x86)] on their c drive, even that isn't necessarily true. I believe also that the name of the folder can change based on localization.
At the very least the extension should display an error when it cannot launch JLink.exe, and allow for the user to manually locate it.