Format time Capsule A1470 hard drive

Getting the new 4TB HDD formatted has been a struggle

Apple never offered a 4 TB version of the Time Capsule. It is either 2 TB (most common) or 3 TB.

The Airport Utility application does not have a format/erase option.

Yes, it does.

Is there an external app that will allow me to format a disk?

The Time Capsule is a "network" drive. You need to use AirPort Utility to erase the disk.

Also, the Time capsule disk is not showing up in the Disk Utility app

It never will. Disk Utility will not display a "network" drive. A lot of other disk utility applications won't either.

The text in the screenshot that you included is too small for me to read accurately.

What is the exact message that you see next to Status? Does it say something about the disk needing repair? If that is the case, the hard drive is defective. It needs to be replaced.

I will pull the HDD out of the TC and format it (externally) with 2 2TB partitions to see if the TC recognized the drive(s).

So far, everything that you are telling us indicates that the Time Capsule hard drive has failed. You can try to format the drive as a last resort, but I would keep my expectations on the very low side.

Let us know how things go. Good luck.

A 4 TB drive is an obvious aftermarket modification. Nothing wrong with that, but if you are bound and determined to make it work suggest you do not partition it. I do not know if the TC will recognize a partitioned drive.

Personally, if I went through the trouble of removing a failed HDD from a Time Capsule I'd replace it with a new one.

👍

Let us know how it works out.