Selfhosted

The best way to run Podman is root with UserNS to dole out UID/GID protection. Running Podman as root allows you to share networks between containers while having the containers run under different users. If you go rootless, you'd need to run under one user to share the user's network space with all the containers you want.

As for your issue, I can't really divine what the problem is from the errors. I avoid nginx because it's coded to not play well with user abstraction and changing the user with the files it wants to write to etc. Gotta write into a ton of random folders! So not sure exactly what is up. But with Podman root it is easy to run as root 0 internally and make nginx think it has all the control it could ever want.

Try this setup (it is in Podman Quadlet format, apologies I don't know the compose versions). It runs the container as root 0 internally, externally it runs as some random UID/GID - secure! It uses Volume idmap to map the internal root 0 user to 1001 for write access to the Volume.

Note that in Debian 13 symlinks are broken and won't work with idmap, just point to the original source. If you need symlinks, I have an alternate UserNS that maps internal user root 0 to external user 1001 directly. You'd drop the idmap in Volume then and use that. You lose some extra security - now the container is running as external user 1001 instead of some random UID/GID - but that's a pretty minor hit as long as your external user doesn't have access to tons of things.

# Volumes to mount -> the @ is essential for saying "1001 is absolute and external" basically. 0 is internal. size of 1. You can map 1001 to 0 and 1002 to 1 with @1001-0-2, etc., etc., etc.  
Volume=/mnt/something:/etc/nginx/wants/to/write/here:rw,noexec,nosuid,nodev,Z,idmap=uids=@1001-0-1;gids=@1001-0-1  

# Run as user running the container  
UserNS=auto  
# [use this if req symlink b/c idmap does NOT work with symlinks] -> I tested and it is fixed in at least Podman v5.8.3, so Debian 14 will work with idmap and symlinks directly ! drop the idmap if using !  
# UserNS=auto:uidmapping=0:@1001:1,gidmapping=0:@1001:1  

# Security time  
NoNewPrivileges=true  
# https://man7.org/linux/man-pages/man7/capabilities.7.html  
DropCapability=all  
ReadOnly=true  
ReadOnlyTmpfs=True  
# These capabilities are needed for linuxserver's s6 "launcher" thing  
#AddCapability=CAP_CHOWN  
#AddCapability=CAP_DAC_OVERRIDE  
#AddCapability=CAP_FOWNER  
#AddCapability=CAP_SETGID  
#AddCapability=CAP_SETUID  
# Needs this if the container tries to bind below port 1024. I'm not sure if it is needed if it only tries to bind internally.  
#AddCapability=CAP_NET_BIND_SERVICE  

# TempFS for ReadOnly fixes I've used for nginx - may not be relevant for you. These are from getting Frigate running.  
PodmanArgs=--tmpfs /usr/local/nginx/conf:size=1M,rw,noexec,nosuid,nodev  
PodmanArgs=--tmpfs /usr/local/nginx/logs:size=40M,rw,noexec,nosuid,nodev  
PodmanArgs=--tmpfs /usr/local/nginx/client_body_temp:size=1M,rw,noexec,nosuid,nodev  
PodmanArgs=--tmpfs /usr/local/nginx/proxy_temp:size=1M,rw,noexec,nosuid,nodev  
PodmanArgs=--tmpfs /usr/local/nginx/fastcgi_temp:size=1M,rw,noexec,nosuid,nodev  
PodmanArgs=--tmpfs /usr/local/nginx/uwsgi_temp:size=1M,rw,noexec,nosuid,nodev  
PodmanArgs=--tmpfs /usr/local/nginx/scgi_temp:size=1M,rw,noexec,nosuid,nodev  
PodmanArgs=--tmpfs /etc/letsencrypt:size=1M,rw,noexec,nosuid,nodev  

Root Podman and UserNS=auto needs a containers user to pull uid/gid from.

# Root Podman needs a `containers` "user" (not really a user, just a reserved uid/gid space)  
sudo echo "containers:2147483647:2147483648" >> /etc/subuid  
sudo echo "containers:2147483647:2147483648" >> /etc/subgid  

The documentation for Podman is critically lacking in the "hobbyist" space. Hope this helps.

Edit: This approach works well because most Docker containers are built assuming they'll run as root 0. That's why Linuxserver uses the S6 overlay thing to jump from root 0 to something else. The container can be built to run as any user though, if you look at the Dockerfile for the container you're using, you'll see what user they're declaring it will run as (and likely what user owns all the files). Root 0 usually gets around that problem - unless they "cleverly" code it to try to prevent you from running the container as root 0 (I've run into this before! It was Heimdall from the Linuxserver people).

Edit2: I've noticed you said no Volumes, so drop that. But you can still use the UserNS mapping to run it as root internally which should fix the internal permissions issues. The tmpfs stuff is if you declare ReadOnly for extra security - it's a great idea - but nginx is extra difficult in that regard. Disregard it while you get going.

# Run as user running the container  
UserNS=auto  

# Security time  
NoNewPrivileges=true  
# https://man7.org/linux/man-pages/man7/capabilities.7.html  
DropCapability=all  
# These capabilities are needed for linuxserver's s6 "launcher" thing  
#AddCapability=CAP_CHOWN  
#AddCapability=CAP_DAC_OVERRIDE  
#AddCapability=CAP_FOWNER  
#AddCapability=CAP_SETGID  
#AddCapability=CAP_SETUID  
# Needs this if the container tries to bind below port 1024. I'm not sure if it is needed if it only tries to bind internally.  
#AddCapability=CAP_NET_BIND_SERVICE  

Edit3:
Use sudo podman top nginx user huser group hgroup groups hgroups to see the internal user/host user (huser) mappings easily for debug.

USER	HUSER		GROUP	HGROUP		GROUPS	HGROUPS  
root		2147485695	root		2147485695	105		105  

Here's an output from my frigate container. Internally (USER) it is root, externally (HUSER) it's some random UID. I've also mapped the internal group (GROUPS) 105 to the external group (HGROUPS) 105 so that it has render access.