🔹 Card-mod - Add css styles to any lovelace card

Erm, what is a difference? Either use mod-card, or apply card-mod directly.
Also, with a hack you can use themes with “card-mod-badge”:

test_badge:
  card-mod-theme: test_badge
  card-mod-badge-yaml: |
    ha-badge $: |
      span.label {
        color: magenta;
      }
      .badge {
        background-color: lightblue !important;
        border: 2px solid red !important;
      }
    .: |
      :host {
        --primary-color: green;
      }
      state-display {
        color: blue;
      }