It looks like you're just missing the {{ body }} loop so you can get the content and sets inside the Bard field. Try this:

{{ if type == 'extended_content' }}
<div class="section-empty">
    <div class="container content">
        {{ body }}
            {{ if type == "text" }}
                <div class="text">
                    {{ text }}
                </div>
            {{ elseif type == "image" }}
                <figure>
                    <img src="{{ image }}" alt="{{ caption }}" />
                    <figcaption>{{ caption }}</figcaption>
                </figure>
            {{ /if }}
        {{ /body }}
    </div>
</div>
{{ /if }}

I tried. Seems like the body keyword knocks out all of the other HTML/Content of every element inside the flexible template. So I changed it to "content" - Now it renders the HTML (also from the other flexible types) but it does not go into the if inside the content loop of the "extended_content"

So if type == "text" will not go into the if.
But when I do {{ type }} it does show all the strings inside the content (e.g text, quote, image, text)

{{ if type == 'extended_content' }}
<div class="section-empty">
  <div class="container content">
    {{ content }}
      {{ if type == "text" }}
      <div class="text">
        {{ text }}
      </div>
      {{ /if }}

      {{ if type == 'quote' }}
      <div class="quote">
        {{ text }}
        {{ cite }}
      </div>
      {{ /if }}

      {{ if type == "image" }}
      <figure>
        <img src="{{ image }}" alt="{{ caption }}" />
        <figcaption>{{ caption }}</figcaption>
      </figure>
      {{ /if }}
    {{ /content }}
  </div>
</div>
{{ /if }}

I also updated the content gist.

What exactly do you mean by the body keyword knocks out all of the other HTML/Content of every element inside the flexible template?

Well, that when I use the {{ body }} {{ /body }} inside the extended_content HTML, none of the other Fieldsets/types render anymore. Basicly the area where the template's html should render, stays empty.

See attached Screenshot. In this example it should actually also render the html of the simple_content type as well

Do you have any other vars named body or content that might be conflicting?