How Does One Add "Humidity" as Secondary Information on Mushroom Dashboard Card?

You are correct! Natively it’s not a card option. Car mod or stacking cards is an alternative method. @Ostrichsak Similar thread here

type: custom:mushroom-climate-card
entity: climate.living_room
hvac_modes: []
show_temperature_control: true
layout: horizontal
card_mod:
  style:
    mushroom-shape-icon$: |
      .shape:after {  
        content: " {{states('sensor.living_room_humidity')}}% ";
        position: absolute;
        left: 155px;
        width: 35px;
        top:18px;
        background-color: transparent !important;
        font-size: 12px;
        font-weight: 400;
        color: yellow;
         }

Hunidity sensor in yellow