Series Ordering

Maybe also check if you have some caching (eg Joomla or server caches) enabled. If so, clear the cache.

So, according to the attachment, the Ordering value is not represented as it should be based on the backend ordering.

Do I just need to manually modify the ordering value?

That's the "hits" column you marked there. The "ordering" is the one with only zeros in it.
Those that have a "0" value, will appear more or less random. In theory, they should be assigned a value when you create/reorder them. I'm not sure why you ended up with zeros.
You can set them directly in the database to the order you want. That will work for sure.

No, it is the ordering field. You can see the value in the actual record itself.

Ah true.

The values actually match to the page displayed in frontend.
The backend looks messed then.
Can you try what happens when you filter the backend list by a single category and then reorder?

No change after doing what you propose.

Looks like it is sorting, in the frontend, based off of category and then order within that category. Only thing I can't figure out is how it's picking the category order to be displayed because even the category ordering in the backend isn't being followed in the frontend.