Tying a few of the pieces here together, here's a straightforward setup based on filebased.EmailBackend. This renders a list view linking to the individual log files, which have conveniently timestamped filenames. Clicking a link in the list displays that message in the browser (raw):
Settings
EMAIL_BACKEND = "django.core.mail.backends.filebased.EmailBackend"
EMAIL_FILE_PATH = f"{MEDIA_ROOT}/email_out"
View
import os
from django.conf import settings
from django.shortcuts import render
def mailcheck(request):
    path = f"{settings.MEDIA_ROOT}/email_out"
    mail_list = os.listdir(path)
    return render(request, "mailcheck.html", context={"mail_list": mail_list})
Template
{% if mail_list %}
  <ul>
  {% for msg in mail_list %}
    <li>
      <a href="{{ MEDIA_URL }}email_out/{{msg}}">{{ msg }}</a>
    </li>
  {% endfor %}
  </ul>
{% else %}
  No messages found.
{% endif %}
urls
path("mailcheck/", view=mailcheck, name="mailcheck"),