@djotaku did you manage to sort this or are you still looking for help? I have been interested in moving over to podman so this post picked my interest (though I admit my attempts were with podman compose and alias masking so it's still a docker setup, though didn't quite work out).
Looking at the config, are you using custom names for the containers? funkwhale_nginx would be funkwhale_front now. But I couldn't help but notice there aren't enough containers? Where are the celerys? For reference, these are all the containers for a stack running on docker:
[upl-image-preview url=https://forum.funkwhale.audio/assets/files/2023-06-07/1686101359-6693-image.png]