Custom UI - icon color change

please try first, and present us with the outcome of your results? scroll down to the end of this post 🔹 Card-mod - Add css styles to any lovelace card - #1188 by Ildar_Gabdullin and see all options.

to get you on track:

          - entity: sensor.backup_state
            card_mod:
              style: |
                :host {
                  --card-mod-icon:
                    {% if states(config.entity) == 'backed_up' %} mdi:check-circle
                    {% else %} mdi:alert-circle
                    {% endif %};

                  --paper-item-icon-color:
                    {% if states(config.entity) == 'backed_up' %} green
                    {% else %} red
                    {% endif %};
                }

adapt to your liking ofc.