Simple Product Listing Pages by Category Slug
You're nearly there! You are missing the part that fetches the entries related to your category.
With your current set up, you would need to do:
{# Get the requested category slug from the URL #}
{% set requestedSlug = craft.app.request.segments|last %}


{# Fetch the category with that slug #}
{% set category = craft.categories()
    .slug(requestedSlug|literal)
    .one() %}

{# Fetch the entries related to your category #}
{% set entries = craft.entries()
    .section('yourSectionHandle')
    .relatedTo(category)
    .all()%}

{% for entry in entries %}
    {{entry.title}}
    {{entry.url}}
    {{entry.image}}
{% endfor %}

Replace yourSectionHandle with, well... your section handle :)
Alternatively, Craft provides a way to simplify the process a bit.

First, it doesn't look to me like you can create separate templates for each category, only the Category group, correct?

You can manually create a template for each category by making a file named as your category slug but this is tedious to maintain.
The way you could handle that would start when you define your category group's settings.
This is only an example but you should get the gist of it.
First, define Settings → Categories → Your Group → Category URI Format to be categories/{slug}, the Template to categories and make a categories.twig template at the root of your templates folder.
Now, when you access yoursite.com/categories/category-slug (category-slug being an actual category slug), Craft will auto-inject a category variable to the template (like the entry variable on entry pages) allowing you to only have the following in the template:
{# Fetch the entries related to your auto-injected category variable #}
{% set entries = craft.entries()
    .section('yourSectionHandle')
    .relatedTo(category)
    .all()%}

{% for entry in entries %}
    {{entry.title}}
    {{entry.url}}
    {{entry.image}}
{% endfor %}

Hopefully, that makes sense for you!