It seems there has been an outstanding issue for this for almost 7 years: https://youtrack.jetbrains.com/issue/TW-10588
As it stands TeamCity does not show any console output for anything that is written in the NUnit fixture setup/teardown methods. Given these can contain arbitrarily complex code it does make trying to diagnose failures in this methods very difficult.
Given TC uses the nunit-console.exe to run the tests, and this program does seem to show the relevant logging there must be something else in what TC is doing which is stopping this info appearing.
Can Jetbrains give us idea of why this logging information does not appear? And if we can have this fixed?
I think also that we do not get the detailed stack trace/failure info for setup/teardown methods that you would normally see for a unit test.