The problem is that you are doing `.relatedTo(category)` but the variable you are passing is called `relatedTo`, not `category`.

Just like with `limit`, based on your code, it should be `.relatedTo(relatedTo)`. Also, it should be part of the same hash as your `limit`.

However, you can't pass a category object to a component and will need to pass its `id` instead ([docs](https://putyourlightson.com/plugins/sprig#component-variables)).

Depending on what `category` is in your case (and I guess it's an object), you could do:

```twig
{{ sprig('_components/load-more', {
    'limit': 6,
    'categoryId': category.id
}) }}
```

Then in your component:

```twig
{% set offset = offset ?? 0 %}

{% set query = craft.entries().section('caseFiles').offset(offset).limit(limit) %}

{# Make sure a categoryId is being passed #}
{% if categoryId %}
	{% set query = query.relatedTo(categoryId) %}
{% endif %}

{% set entries = query.all() %}

{% for entry in entries %}
   ------Entry Content-----
{% endfor %}

{% if entries %}
  {# Increments `offset` by the value of `limit` and swaps itself out on click #}
  <button class="orange-button" sprig s-vars="offset: {{ offset + limit }}" 
    s-target="this" s-swap="outerHTML">
    <p>Load More</p>
  </button>
{% endif %}
```