Reads to me like the container it's running as a user that doesn't have permission to the volume path.

Probably just a permission issue. The doc seems to recommend giving relaxed permission to the temp folder volume:

sudo chmod 777 /your/linguacafe/temp/folder -R

Did you change the mysql container database name, username and password to something other than the default linguacafe ?

That would break it, as it's using those specific credentials to login to the database. Which would cause Access denied for user ‘linguacafe’@‘ip adress censored’ (using password: YES) (SQL: select count(*) as aggregate from users)

Try with the default, you'll need to wipe the mysql data under /home/user/Documents/Docker/LinguaCafe/database/ after stopping the container first.

    environment:
        MYSQL_DATABASE: linguacafe
        MYSQL_USER: linguacafe
        MYSQL_PASSWORD: linguacafe
        MYSQL_ROOT_PASSWORD: linguacafe
        SERVICE_NAME: linguacafe

You seem to be missing your username in the volume paths, e.g. /home/username/Documents.

That error message says it the permissions of the /home/user/Documents/Docker/LinguaCafe/logs directory. You can try changing it full r/w temporarily to test.

I think I solved the permission issue? See edit in the main post.

Based on your update you may need to bring the containers down and up to fix the database.

Sometimes when opening LinguaCafe the first time there is an error message about users database table. If this happens, just stop and start your containers again, it should fix the problem.

docker compose down
docker compose up -d