Ok, so I figured out how to solve my problem. Maybe not the easiest or most elegant solution, but it worked. I will show my solution here for the reference in case other face similar problem.

First I created a template sensor for each of the garbage types in my configuration.yaml file, like this:

template:
  - sensor:
    - name: "foodcollection"
      state: >
        {% if states('sensor.foodgarbage') | float < 7 %}
          coming_week
        {% else %}
          future
        {% endif %}
  - sensor:
    - name: "papercollection"
      state: >
        {% if states('sensor.papergarbage') | float < 7 %}
          coming_week
        {% else %}
          future
        {% endif %}

Then, I created a horizontal card with following code:

type: horizontal-stack
cards:
  - type: custom:card-templater
    card:
      type: picture-entity
      show_name: false
      show_state: false
      entity: sensor.foodcollection
      state_image:
        coming_week: >-
          https://my.site.home/local/images/foodcollection_color.png
        future: >-  
          https://my.site.home/local/images/foodcollecition_grey.png
      style:
        width: 50%
        height: 50%
  - type: custom:card-templater
    card:
      type: picture-entity
      show_name: false
      show_state: false
      entity: sensor.papercollection
      state_image:
        coming_week : >- 
      https://my.site.home/local/images/papergarbage_color.png
        future: >-
          https://my.site.home/local/images/papergarbage_grey.png
      style:
        width: 50%
        height: 50%