I'm not sure if it's related to your issues, but the first thing I tried was to update to the last v3.1x release. According to Mayan docs that should be v3.1.11 but when I tried to update to that, I got this error:

Collecting mayan-edms==3.1.11
  Could not find a version that satisfies the requirement mayan-edms==3.1.11 (from versions: 1.0rc1, 1.0rc2, 1.0rc3, 1.0.0, 1.1.0, 1.1.0.post1502100955, 1.1.1, 2.0.0b1, 2.0.0b2, 2.0.0rc1, 2.0.0, 2.0.1, 2.0.2, 2.1rc1, 2.1rc2, 2.1, 2.1.1, 2.1.2, 2.1.3, 2.1.4, 2.1.5, 2.1.6, 2.1.10, 2.1.11, 2.2b1, 2.2b2, 2.2b3, 2.2rc1, 2.2, 2.3, 2.4, 2.5, 2.5.1, 2.5.2, 2.6, 2.6.1, 2.6.2, 2.6.3, 2.6.4, 2.7, 2.7.1, 2.7.2, 2.7.3, 3.0, 3.0.1, 3.0.2, 3.0.3, 3.1, 3.1.1, 3.1.2, 3.1.3, 3.1.4, 3.1.5, 3.1.6, 3.1.7, 3.1.8, 3.1.9, 3.1.10, 3.2b1, 3.2rc1, 3.2, 3.2.1, 3.2.2, 3.2.3, 3.2.4, 3.2.5, 3.2.6, 3.2.7, 3.2.8, 3.2.9, 3.2.10, 3.2.11, 3.3, 3.3.1, 3.3.2, 3.3.3, 3.3.4, 3.3.5, 3.3.6, 3.3.7, 3.3.8, 3.3.9, 3.3.10, 3.3.11, 3.3.12, 3.3.13, 3.3.14, 3.3.15, 3.3.16, 3.3.17, 3.4, 3.4.1, 3.4.2, 3.4.3, 3.4.4, 3.4.5, 3.4.6, 3.4.7)
No matching distribution found for mayan-edms==3.1.11

So i fugures that I might as well just upgrade to v3.1.10 fo starters... Here's the full commands I ran:

REMOVE=/etc/mayan/removals.txt
curl https://gitlab.com/mayan-edms/mayan-edms/raw/master/removals.txt > $REMOVE
supervisorctl stop all
ENV=/etc/mayan/env
BIN=/opt/mayan-edms/bin
su - mayan -c ". $ENV && $BIN/pip uninstall -r $REMOVE"
su - mayan -c ". $ENV && $BIN/pip install --no-cache-dir mayan-edms==3.1.10"
supervisorctl start all

Note that the '-no-cache-dir' switch just stops this warning:

The directory '/.cache/pip/http' or its parent directory is not owned by the current user and the cache has been disabled. Please check the permissions and owner of that directory. If executing pip with sudo, you may want sudo's -H flag.

After I've run that, I logged in via the web browser and everything seems to "just work"?! The about page (/#/about/) reports that the version is v3.1.10?! Obviously my copy doesn't actually have any data in it, but it all seems to be working ok?!

I wonder if there is some sort of issue with your browser caching info? Perhaps try doing a "hard refresh" (to clear cache and cookies) - usually that is by holding Control and hitting f5. And/or try loading Mayan via a private/incognito browser session (by default will disable browser addons/extensions and will have no cached data or cookies).

FWIW I can reproduce your issue.

I'm not 100% sure what the cause is, but after upgrading to v3.2, when I clear all my browser cache and cookies and go to my server in my browser, I'm getting a weird redirect loop with a URL of:

https://MY_SERVER_IP/authentication/login/?next=/#/authentication/login/?next=/

Although, when I opened the "developer console" I notice this message is showing (between the redirects):

Server error
There's been an unexpected error.

What to do next?
 - Refresh the page.
 - Wait a bit. The system might be overloaded.
 - Contact your system administrator.
 - Check the logs for messages with the tags "ERROR", "CRITICAL" or "FATAL".
 - Open a ticket using the issue tracker.

If I look in the system journal (i.e. journalctl) it seems clear that the Mayan supervisord services are crashing and being restarted. There are also Python errors being noted in the Supervisor logs (files in /var/log/supervisor/). So it seems clear that there are some python errors occurring.

I've messed up my server so bad now, I probably need to start again...

FWIW, I'm not sure if it's related at all, but when I try to run the DB migration, it throws an error too.

It may be possible to simply migrate the data/documents to a new install? Actually, seeing as the old Mayan appliance was using Python2 and (when we get to it) the new Mayan appliance will use Python3, perhaps now is a good time to look at that migration?!