The django-modeladmin-reorder library looks like it is not maintained, with issues (e.g. the issue already raised in early 2020 for nav-bar customization) in the github repo remaining unanswered for 2 to 3 years now. This affects the nav-bar customization, which is supposedly support by the library.
Thankfully, in the same issue, given as an example above, a user has provided their local repo for which they are handling the nav-bar functionality. Unfortunately, despite having a PR created, this is not accepted (at the time of writing this).
If you already using the library, moving from the library to the local repo should be easy and nearly plug'n'play. All you have to do is uninstall the library that you already use for the reordering:
pip uninstall django-modeladmin-reorder
Then you can re-install it through the local report:
pip install git+git://github.com/bloodwithmilk25/django-modeladmin-reorder.git@master
If that fails you can try to change git+git to git+https:
pip install git+https://github.com/bloodwithmilk25/django-modeladmin-reorder.git@master
Then all you have to do is to re-run your server and changes should be available both in the homepage and in the nav bar.
Disclaimer: I have no affiliation to the library or the repo of the user. I was simply trying to find a solution for a couple of days and I found this. I thought to create a question and answer it myself, to let the world know. There is no provision or expectation that the repo will be maintained properly for future version of Django and/or Python. Though, this is the best alternatively that we have now, unless someone wants a completely customize solution (which this repo can serve as a guide either way). Hopefully the user's PR will be accepted and we will be able to move back to the library.
My custom homepage

My custom nav bar
