First of all, sorry for the late reply.
We have been investigating it, and we can't find the source of your issue by checking the information that you have sent to us.
There should be some misconfiguration in the Site Url. You can check it in
General Settings. Is the
Site Url field the same that you are using when accessing your application?
A different option to upgrade your application is doing it by command line. As this method doesn't imply interaction with the web browser, you should not face the redirection loop issue that you are experiencing. Follow the steps described in this guide: Uh Oh, Mautic upgrade was not successful. In particular, we have tested it and this is what we needed to do to upgrade a Bitnami Mautic Stack
2.13.1 to the latest version:
IMPORTANT! Please do a backup of your application before you run any of the below steps. Create And Restore Application Backups.
1) Connect to the server through SSH.
2) Execute the following commands. Note that some of them will prompt for confirmation:
sudo su daemon -s /bin/bash -c "/opt/bitnami/php/bin/php app/console cache:clear"
sudo su daemon -s /bin/bash -c "/opt/bitnami/php/bin/php app/console mautic:update:find"
sudo su daemon -s /bin/bash -c "/opt/bitnami/php/bin/php app/console mautic:update:apply"
If any of the above works, would it be a possible option for you to launch a new server with the latest version of Mautic (https://bitnami.com/stack/mautic/cloud/aws) and migrate the data from a server to the new one?