Change header logo image based on product/collection tags?

I am aware that I will need if and else but I am using Warehouse 2.0 and the information about the header image is in a capture so I am unsure how to do it.

{%- capture header_logo -%}
          
            {%- if section.settings.logo != blank -%}
              {%- capture image_size -%}{{ section.settings.logo_max_width }}x{%- endcapture -%}
              {{ shop.name }}
              
            {%- else -%}
              {{ shop.name }}
            {%- endif -%}
          
        {%- endcapture -%}

        {%- if request.page_type == 'index' -%}
          # {{ header_logo }}
        {%- else -%}
          {{ header_logo }}

        {%- endif -%}

Is it perhaps related to the if request.page_type section?

I have set up custom page and collection and product templates with their own name.