Magento 1.7 – Search Results Show Filters, Category Pages Do Not

I don't know how your extension is built, so I cannot provide any code but here is an idea on wow you can do it.
In a search page this piece of code will return null always:

Mage::registry('current_category');

In a category page this will return a category instance. You can use this in your own block. So for each method you override you can do the followin check before doing something. Let's say your method is called doSomething(). In your block it could look like this:

public function doSomething($someParam) {
    if (!Mage::registry('current_category')){//not on category page
        //call the default behavior
        return parent::doSomething($someParam);
    }
    //your custom behavior here
}

You can even change the template that renders the block this way:

public function __construct()
{
    parent::__construct();
    //by default the template 'catalog/layer/filter.phtml' will be set
    if (Mage::registry('catalog_category')){//if category page
        //set your custom template with price slider.
        $this->setTemplate('custom/template/here.phtml');
    }
}

I would say that the toolbar is not being loaded at all on the search results pages. Enabling template path hints will let you check to see if the block is being outputted to the page.

If it isn't being outputted you will want to check your theme xml and list.phtml files.

Assuming your results pages use the same template as your category pages (standard), the file YOURTHEME/template/catalog/product/list.phtml should have the following line in it:

<?php echo $this->getToolbarHtml() ?>

If it does have this line you will need to check your theme xml files to see if the block has been removed catalogsearch.xml, or overwritten in the theme's local.xml