An example of running a container with non-root user and mounting volume in a way it can write to it.
Build:
podman build -t container-owner-example .
Check it works:
$ podman run --uidmap 1001:0:1 --uidmap 0:1:1001 -v $(readlink -f shared):/shared --rm -ti container-owner-example ls -al /shared
drwxr-xr-x. 2 testuser testuser 4096 Jun 7 14:16 .
drwxr-xr-x. 20 root root 4096 Jun 7 14:22 ..
-rw-r--r--. 1 testuser testuser 21 Jun 7 14:16 ahoj
-rw-r--r--. 1 testuser testuser 6 Jun 7 14:16 ahoj2
-rw-r--r--. 1 testuser testuser 4 Jun 7 14:16 ahoj3