@erieberrie for apps just search the app store for request/free sample apps you’d have to shortlist which ones can organize into collectins.
Meanwhile for that example site all that is is an HTML mailto link styled as a button which you can do in a lot of themes using a custom-liquid or custom-html block.
If you need this customization tailored for you then contact me directly by mail for services.
Please always provide context, examples: store url, theme name, post url(s) , or any further detail.
Contact Info in signature.
{%- comment -%} © 2023 Paul Newton. paull.newton+shopifyforums@gmail.com {%- endcomment -%}
{%- liquid
sample_link_text = "Request a sample"
sample_email = "paull.newton+shopifyforumssamples@gmail.com"
sample_subject = "Sample Request" | url_encode
sample_title = product.title
sample_body = "Please provide me with a sample for " | append: sample_title | url_encode
-%}
{% assign %}
[
{{ sample_link_text }}
](mailto:{{sample_email}}?Subject={{sample_subject}}&body={{sample_body}})