How do I use start-app template context in a template file?

Question

I have the current setup for a Django app template which I pass to start-app like so:

python3 manage.py start-app --template template/ myapp

With a directory structure like this:

template/
    templates/app_name/
        page.html
    ...
    app.py

app.py uses the template context passed when start-app is run, and works fine!

# app.py
from django.apps import AppConfig

class {{ camel_case_app_name }}Config(AppConfig):
    default_auto_field = 'django.db.models.BigAutoField'
    name = '{{ app_name }}'

However, I'm trying to get similar behaviour out of page.html, to no avail.

{% extends "{{ app_name }}/otherpage.html" %}

{% block content %}
   <p>Hello from {{ camel_case_app_name }}!</p>
{% endblock %}

If I run start-app like normal, the template is copied over and the app name is not inserted. If I try to run start-app with --extension py,html I don't get the expected behaviour either, because the template is rendered.

Is there a way to convert the {{ app_name }} calls in page.html without attempting to render the entire template?