json_attributes is looking at the root of the json data. Which is not where max and day are. Hence you are getting no attributes for sensor.own_report, only a state. You need to supply a path to the attributes:
- platform: rest
name: own_report
json_attributes_path: "$['daily'][0]['temp']"
json_attributes:
- max
- day
resource: https://api.openweathermap.org/data/2.5/onecall?lat=*****169&lon=*****1406&lang=it&APPID=*****&units=metric&exclude=current,minutely,hourly,alerts
value_template: "{{ value_json['daily'][0]['temp'] }}"
A better way to do this, without the need for template sensors would be to use the new rest platform to create as many sensors as you want from the one call to the resource:
Including state_class give you access to long term statistics, this is optional.
Including device_class makes the sensor look pretty in Lovelace (adds a unit of measurement and an icon), again this is optional. You can provide your own unit_of_measurement and icon if you prefer. Though you would have to add the icon via customize as it is not a configuration option supported directly in the rest platform. Much easier to use device_class in this case.
The restful integration does not. You can have as many sensors as you want for the one resource and they will all be updated from each single call to the resource. That was the whole point behind developing it as an integration.