Fix Interactive container hangs when redirecting stdout

Fixes #6509
Closes #7658

This is a rebase of #7658 + tests. Thanks @VojtechVitek !

I even tested the `events` test with one commit before the #5979 PR and it failed. So all 3 are needed.

Ping @erikh @jfrazelle
Can this field have docstrings which describes difference between them?