The Django application listening on the unix socket uses a different protocol than HTTP, most probably FastCGI. So you cannot use an HTTP client to talk directly with it.
Here you can find an article showing how to use a command line program called cgi-fcgi to talk directly with your application. The article uses Php-fpm, but the concept is the same.
Django test module has a Client that can talk to a wsgi/asgi application.
You can probably use this in a REPL python session for instance.
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