Installed Catalina, now can't backup with TimeMachine-only format APFS

Firstly, you cannot use Case-sensitive for a macOS disk. Secondly, follow this:

Drive Preparation - El Capitan or Later

1. Open Disk Utility in the Utilities' folder.
2. After Disk Utility loads select the drive (out-dented entry with the mfgr.'s ID and size) from the side list. 
3. Click on the Erase button in the Disk Utility toolbar. A panel should drop down.
4. In the drop down panel set the partition scheme to GUID. Set the Format type to APFS (SSDs only) or Mac OS Extended (Journaled.)
5. Click on the Apply button and click on the Done button when it is activated.
6. Quit Disk Utility.

You should be able to choose Mac OS Extended, (Journaled) in the panel that drops down after clicking on the Erase button in Step 3.

Examine the drive listings in Disk Utility. You will see SSD in the topmost item of a drive's listing in Disk Utility. For example,

Note the topmost item for the drive says, "Apple SSD...". This is usually what is shown about an internal drive. May not be the case for an external drive whose topmost item may refer to the manufacturer of the enclosure.

Out-dented refers to the topmost entry - WD My Book 25EE M.... The Container disk5 is an indented entry as is the WD Time Machine entry. To just erase and reformat a volume such as WD Time Machine select that volume to reformat. You can leave it using APFS, if it's an SSD, because that selection is not case-sensitive.

Didn't see this post when I responded, so you should ignore my reply. Because the drive was already setup as an APFS drive, the partition scheme was set as GUID already. You won't see it again unless you partition the drive. Although a Container works a little like a partition, it is not strictly a partition. Rather it's a reservation of space. Without limiting parameters Containers can be of any size up to the capacity of the drive. Containers have some flexibility in how small or large they are making multiple them expandable and contractable depending upon how much file space is used.

Containers may be limited in size at the time they are created. For example, I have a drive with two containers. The second container has been setup such that it only can use 480GBs of space. The remainder belongs to the first container. Essentially, I created two partitions in the form of two containers. The same can be done with the volumes within a container.

I do not think you need a new install. Did your iMac come with a Fusion Drive - an HDD and a small SSD? I need to know that before giving you a possible solution. Do I assume that you inadvertently erased Macintosh HD? If not, then how is it messed up? You have installed Catalina on an APFS formatted disk. Catalina creates a startup disk that has two volumes within the initial container. One volume, Macintosh HD, is visible on the Desktop. The second volume, Macintosh HD - Data is not visible. macOS is installed on the first volume which in turn is locked against all access including the Admin user. The second volume contains all the rest of macOS and all the users' files and data. Unix hard links are created so that the user accesses the visible volume exactly as it has always been accessed. The OS is protected from any alterations intended or unintended, making it more secure and less vulnerable to damage.

What you see in the image above is exactly what you should see in Disk Utility, but not visible on the Desktop. The two volumes share the first container which becomes identified as "disk2" even though such a disk does not physically exist. It's referred to as a "synthesized disk." There are three other volumes in the container that are also invisible: Preboot, Recovery, and VM. Recovery is the same as the Recovery HD used to repair, reformat, or reinstall macOS. The other two are used by APFS and macOS.

I need answers to my first couple of questions so I don't send you on a wild goose chase. You can downgrade back to Mojave provided you still have a full Mojave installer. Then you must erase the drive in order to reinstall Mojave. But if that's your preference, then I can show you how it's done.