When making a new paragraph, is it possible to make them inherit the base styling and settings of our paragraphs?

By making new ones, you lose the extra functionality that was added via the profile_paragraphs module to these specific paragraphs. Eg. the visual background-color selection field.
That is one thing we can't really fix. But since the field already exists, just reuse them.

However, new paragraphs don't inherit the basic twig file(s). So find way around this (have paragraphs always use same field template)