Okay, until there is some more flexibility added to Jellyfin in this regards, our solution:
G_CONFIG_INJECT 'JELLYFIN_LOG_DIR=' 'JELLYFIN_LOG_DIR=/mnt/dietpi_userdata/jellyfin/log' /etc/default/jellyfin
G_CONFIG_INJECT 'TMPDIR=' 'TMPDIR="$JELLYFIN_CACHE_DIR/temp"' /etc/default/jellyfin
The log file is rotated automatically by Jellyfin, see /etc/jellyfin/logging.default.json. I would have preferred to disable file logging completely, since it is just a duplicate of journalctl -u jellyfin syslogs. There are even two config files /etc/jellyfin/logging.default.json and /etc/jellyfin/logging.json where this is defined. But Jellyfin internally seems to always merge the config arrays with defaults, which contain and hence readd the "async" file logging entry.
The TMPDIR change basically restores the behavior from Jellyfin pre-10.10, where a temp subdir of the cache dir was used, not /tmp: Use real temp dir instead of cache dir for temp files (#12226) · jellyfin/jellyfin@c666f9d · GitHub
There is even a hint about exactly that in the env file /etc/default/jellyfin.
EDIT: Fixed with: dietpi-software: Jellyfin: fix install due v10.11 changes · MichaIng/DietPi@ce6a02f · GitHub