How can I act on a taxonomy term in my twig template?
content.field_taxonomy_resource_type is a render array, which you're comparing against a string. Instead, you need to get access to the label, and extract the term name.

Try this instead (if in a node template):

{% if node.field_taxonomy_resource_type.entity.label == "Topic Page" %}


Or, as we know it's a paragraph template:

{% if paragraph.field_taxonomy_resource_type.entity.label == "Topic Page" %}