try to figure out how to configure our application to work in this setup itself (not sure how much developer effort will be needed)
use the hosted fief instance. This could work, as long we use different instances for development and production.
make our own authentication service. This would give us a lot of flexibility, but will have A LOT of things to consider to ensure safety. Personally do not recommend.
So the way that Fief is made, is that it requires a subdomain to properly work. This is also mentioned in the discussion here: https://github.com/orgs/fief-dev/discussions/93
If we are to follow this, then we will need to figure out how to make this work in Docker Compose, Nginx, etc.