With some inverse modification to continue(autoskip ) part of a loop, you would take the logic you’ve put together and find the article loop in whatever the “blog section” is for your specific theme. And wrap that logic with your logic.
Do the tag check like your doing but when it’s NOT a match use the {% continue%} tags to make the current article that doesn’t have a tag match get skipped.
{% if article.tags contains product_handle %}
{{ article.image.src | img_url: 'large' | img_tag: article.title }}
{{ article.title }}
{% else %}
{% continue %}
{% comment %} The rest of the default article code goes here inside the else & endif {% endcomment %}
{% endif %}
Keeping in mind that contains makes matching tags fuzzy so trying to match “contains red” would also match any tag with those characters so a “credit” tag would create a false positive.
https://shopify.dev/api/liquid/tags/continue
If you need this customized for you then contact me , info in sig. Please provide context: store url, theme name, post url and detail.