Picture elements cards support the use of css styles without card mod.
Entities cards require card mod.
This simple test shows that card mod is not installed correctly.
Also you can not use templates in Lovelace without installing one of the custom template cards. Do you have one installed?
The jinja template card has a large performance overhead. I would not recommend it.
The javascript template card is a better option.
But fix card mod first.
Until you can get this working, card mod is not installed correctly:
type: entities
style: |
ha-card {
color: red;
}
entities:
- sensor.internet_ping