I remember doing this with an older nook. To get my sideloaded books (via Calibre) show up in my Library instead of My Files, I need to put them in a specific folder.

Does this still work, and what is the folder?
I have a 2015 Glowlight Plus. It may be a little different than what you see on the Glowlight 4.

I put all the books in the Nook folder on the device. But I think what matters most are the settings in your Nook library. I my library, on the top left there is a text link that you can click on. It offers to show you All Types, Books or My Files. I set it to All Types.
There used to be a way to get the books to show up under "Books" instead of My Files. I just don't remember how to do that.

I seem to recall something about using adb to load the books onto the nook.
On my Glowlight 4, I have my sideloaded books in the mnt/sdcard/NOOK folder so that they will show up in Library in the Nook reader. I also have a different launcher and other Android reader apps installed for when I want to use those. Some time ago, I blocked firmware updates so that B&N wouldn't mess up my setup! That said, I don't know if the current B&N firmware works in the same way.

My Glowlight 4 is rooted, so I can sideload books in a number of ways.
If the Glowlight 4 was mine, I would root it and install all sorts of stuff. But since my wife uses it every day, there is no way I'm messing with it.

When my wife got her first nook, the one with the color screen on the bottom, I rooted it and installed an alternate reader that sorted books into folders based on series names. She was not happy with me.
Actually, you can install another launcher and other apps without rooting it. You need root only if you want to make changes at the root level. In my case, I wanted the page turn buttons to work for third party reader apps. I needed root to make that happen.

However, even that would add a step or two (such as choosing your launcher at startup) that might not go over well with your wife!
Is there a simple way to change the Nook firmware to easily repartition the amount of space for sideloading? Similarly, is there any way to access the database to set series info for sideloaded content?

I'm actually okay with the out of the box Nook firmware, if I could just change those two things.
If, by a "simple way" you mean a way that can be easily followed by the typical device user who loves to read but who has never had any occasion to learn about rooting, adb, or similar incantations, the answer, sadly, is no. When it comes to repartitioning, someone could come up with a step by step guide. However, the problem is - with due apologies to Paul Simon - "there must be fifty ways to brick your Glowlight" if you make a mistake. People who are experienced with the above incantations also make mistakes - shocking as that revelation may be! The difference is that they can figure out what their mistake was and then how to rectify it. The typical device user, following a guide and then making a mistake, does not understand what went wrong and hits a wall. It seems unfair to do that to anyone - unless that person is willing to ask for help on a forum like this one and work with a more experienced person to get the repartitioning done.

(I could have been more concise and simply said no, but where's the fun in that?)
That's a shame. I like my Nooks and if there were a few tweaks I'd like them as much as Kobo.
I think nooks are a great value. I just wish they didn't treat side-loaded content like read-headed stepchildren.

With Apprentice Alf losing the ability to liberate nook files, we've been doing far more purchases on the Kindle so more stuff ends up sideloaded on the nook.

I've given my wife my Kindle to use. It has a bigger screen and she prefers the nook. I wish the Paperwhite had page turn buttons.