Hi, and Welcome to Azeroth! 
Yes, you gave a very clear description.
I don’t know the answer exactly, because I don’t use bags that way myself, and my First Rule of Bags is: NEVER hit the Clean-Up button or allow the game to decide ANYTHING about my bags! P
There is a circular bag icon at the top left of your combined bags. If you right-click that, you will get a menu with options, and I would suggest that you turn off Clean-Up Bags wherever it appears. I don’t think the built-in bag UI can do what you want, though.
The devs of WoW decided long ago to leave the UI open for people to arrange their view of the game however they want, using Addons written in Lua that call the API, rather than write a very configurable UI themselves.
So I think your best bet is to install an Addon to customize your bags the way you want.
Bagnon is the biggest and best addon for displaying bags, and I am sure it can help you out here. It has its own options for displaying the contents of bags.
Now, you’re hitting Addons earlier in your WoW career than maybe most people do, and there’s a bit of setup involved, so engage patience. Take a deep breath! 
There are two aspects to Addons: 1. Choosing and installing them and 2. Keeping them updated. Most people install an Addon Manager for this. An Addon Manager is a program you install on your PC that installs Addons, and that regularly checks for new versions to update them.
I use WoWUP as my Addon Manager (you can just google it) but most people use the Curseforge app WITHOUT Overwolf. (Don’t ask; just avoid the version with Overwolf).
Once you have installed your Addon Manager, you can just ask it to search for and install Bagnon.
This is a HUGE video that tells a beginner lots and lots of things about WoW that you will want to learn. It’s two hours long, but broken up into 1-2 minute chapters introducing each sublect. I have teed it up to the section on Addons, and it will lead you through installing the Curseforge Addon Manager
https://www.youtube.com/watch?v=nnzdeoSMkvM&t=6259s
It’s worth bookmarking that video, or maybe even watching chunks of it now that mean something to you, because there’s a LOT of great information there!
Once you have installed Bagnon, you can get up its configuration options by typing
/bagnon
into your chat box or by
- hitting Esc to get up your Game Menu
- Choosing Interface
- Hitting the Addons tab at the top right
and selecting Bagnon in the list.
PLEASE ask again if you hit a problem with any of this.
P.S. Afterthought
If you install an Addon Manager, that’s the hard bit done, so you might be tempted to install ALL the addons 'cos they all seem to do AMAZING things! 
Um.
Take it slow, and keep control of your addons. You may suddenly see strange things happening that you do not understand, did not want, and do not control. I always suggest that you install addons one by one - install one, learn it, understand it - then add one more, learn it, understand it. If you add 15 together like a kid in a candy store, the result will be … cacophanous! 
Remember that you can also remove addons with your Addon Manager, and you can disable them one by one in the Addons section of your Game Menu.