Card Mod and Tabbed card won't work

Have you tested these templates in Dev tools → Template?
Can you test with a simple ONE tab inside tabbed-card, containing one Picture-elements with ONE icon and w/o these templates?

Sure, but people here are mainly not interested in finding differences, this is YOUR work to present a task in a clear form.

And this a short example which you may use:

type: custom:mod-card
card_mod:
  style: |
    ha-card {
      background: cyan;
    }
card:
  type: custom:tabbed-card
  attributes:
    icon: mdi:circle
  tabs:
    - card:
        type: picture-elements
        elements:
          - type: state-icon
            entity: sun.sun
            style:
              top: 50%
              left: 50%
              "--card-mod-icon-color": var(--some-var)
        image: /local/images/test/orange.jpg
        card_mod:
          style: |
            ha-card {
              --some-var: red;
            }
      attributes:
        label: xxx


Just provide your own simple background image.