How do I render a page as part of another page

I don’t know what to tell you. I just tested it, just in case, and I was able to access extra variables as expected.

Perhaps your Tera logic needs fixing? If not all posts have a particular extra variable, you need to first check whether it exists.

For example, this will fail if a single post doesn’t have the foo variable:

Post's foo: {{ post.extra.foo }}

This will work:

{% if post.extra.foo %}
Post's foo: {{ post.extra.foo }}
{% endif %}

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