... /system has no space left.
It indicates that your
/system partition is mounted R/W but just to make sure, if
dm-verity is enabled,
/system is always R/O. For details see How to disable dm-verity on Android?.
Next, both of your screenshots show that your
/system partition is full. Even if you haven't written anything to it, some ROMs may have
/system already completely filled. After all it isn't for user's usage.
The space shown as "System" in Settings isn't actually the
/system partition. In fact it can't be of 11GB, that's too much. Android is counting a large data from
/data partition also as "System", because it's not what a "user" directly puts there. User can access only shared/external storage (
You can check actually space usage of
/system partition with command
df -h /system. Execute
du -h /system | sort -h to get a directory-wise detail of what's taking up space.
For more details, see How disk space is used on Android device?