The image is string so you can’t use templates there.
What you can do is to link to a static image/webpage and then replace the image on that image/webpage.
If you are trying to display the most current snapshot on your dash AND the counter resets after x amount of snapshots, you can use local file entities with conditional cards. Where each snapshot had it’s own local file entity. If the counter just continues to increase this will not work.
Use the counter as the entity in the conditional card. If the counter was at 5 you would use
It would display the card with snapshot 5 and hide the others.
Unless something has changed www did not need to be added to the allowlist_external_dirs. It is shared by default. I don’t have it in my allow list and I was able to add the sensor and write to a file in a sub directory of www. Perhaps remove the entry from allowlist_external_dirs.
If things haven’t changed /www is not a good place to store photo as it is not protected by HA’s auth system. I use /media for snapshot storage, that path needs to go in the allow list.