It could indeed be the issue.
I am not very familiar with Debian, but you do have ProtectSystem=full in your service file.
Take a look at this, it was kind of a similar problem.
You may need to adjust ReadWritePaths accordingly and add the folders Caddy uses to store its data and logs.
Refer to the following:
or check your Caddy debug log to see where it is trying to store data.
Also, make sure caddy has read/write access to those folders.