Hi Martin,
I'm so sorry we haven't gotten back to you until now. Between our private support channel and the upcoming Review Board release, we've been stretched a bit thin this past week. I don't know if you've gotten any further at this point, but I can try to help you get unstuck.
Review Board 4 does work with Python 2.7. You don't need Python 3. Review Board 5.0 and higher will require Python 3, so it's still worth doing.
However, your system is only configured to run Apache with Python 2.7. So your attempt to install the Python 3 versions (using pip3) isn't going to work at this stage. Depending on how old your distribution is, you may or may not be able to switch this to Python 3. It could require a new install (I'll talk about that in a minute).
For now, you may want to just stay on Python 2.7.
Now, the py31compat issue. I've seen this before. It's a third-party issue that's common on some versions of Ubuntu, due to a packaging problem of theirs. It's affected a lot of Python-based software.
You can try to install the official setuptools package (which provides pkg_resources) via pip, and see if that addresses it. You may also need to remove or move aside the old version shown in that error output.
To try to install the official version:
sudo pip install -U setuptools
Then restart Apache, see if the error changes. It very well may not, in which case you'd have to see if moving /usr/lib/python2.7/site-packages/pkg_resources/ elsewhere does any good (I wouldn't outright delete it though, in case you need to undo this).
At some point, maybe sooner, you probably should consider a new Linux install built for Python 3. You'd have to go through our guide and set up all the packages from scratch. What you'd then do is, instead of running 'rb-site install', you'd copy over the old server's site directory (what you pass to 'rb-site') and Apache configuration. Get those in the right place, then 'rb-site upgrade' that. Since you've already gone through that 'rb-site upgrade' process with your current database, this should be quick, just setting up some state for your new server.
We do provide support contracts, if you'd like details on that at any point. We can help with upgrade planning and be on call when it's time to move things over.
Christian