USB External HDD not appearing on Network via Time Capsule

The external HDD is formatted APFS and appears in the Finder and Disk Utility when connected directly to my Mac. However, it does not appear in Disk Utility, Airport Utility, or Time Machine preferences when connected to the Time Capsule via USB

The USB port on the Time Capsule does not support APFS. Your only option would be to format the drive as Mac OS Extended (Journaled).

Then, Time Machine has to try to convert data stored on the Mac's drive in APFS to be stored within an APFS formatted sparsebundle file on the Time Capsule disk, which is formatted as Mac OS Extended (Journaled).

Gosh, I wonder what could go wrong with a goofy setup like this. My advice.......don't keep anything that you cannot afford to lose on the USB drive connected to the Time Capsule.

Keep in mind that the USB port on the Time Capsule is underpowered, so you may need to use a powered USB hub with the USB drive.......even if the USB drive has its own power supply.

When the USB drive is formatted correctly in Mac OS Extended (Journaled)......and......the USB port on the Time Capsule is supplying adequate power, the USB drive will show up in AirPort Utility under the "Disks" tab along with the Time Capsule drive......likely named "Data" unless you have renamed the drive.

Also keep in mind that the USB port is an ancient USB 2.0 design, so backups are going to run at about half of the normal speed backing up directly to the Time Capsule disk.

Two possibilities:

The Synology router and upper end Asus routers all have a USB 3.0 port that will support Time Machine backups. So, instead of a one-piece router/hard drive solution with a Time Capsule, you will have a two-piece solution.......a router with a separate attached USB drive that can be used for Time Machine backups and other storage.

Probably a better.....but more expensive solution would be to look for a new WiFi 6 router that will handle all your routing duties and connect a NAS via Ethernet to the router. Synology is a popular choice for Apple users because it fully supports Time Machine backups.

If you don't need a new router, the simplest and most reliable connection by far would be to connect the USB drive directly to your Mac and back up that way. If you have a laptop and don't want to haul the USB drive around, maybe you could back up once a day.

Are there any alternatives to a new router and a NAS?

Apple is pushing everything to iCloud services. Unfortunately Time Machine is still limited to local network or directly plugged in drives.

I think they will eventually get there.. so TM will no longer backup your Mac OS as that would just be wasted space in cloud, but all your user files and settings etc.

For now the best option is a USB drive plugged directly to the computer.. in your case a charging USB hub could be used instead of Apple charger and provide fixed USB drive for any occasion the laptop is charging.

As far as network backups go.. your choice is NAS for a number of reasons..

Routers including Apple Time Capsule do not support SMB3. That is the protocol default used by Apple since Sierra. Backups to Time Capsule still work over the AFP protocol and routers like the Synology or Asus etc that support TM backups. Only NAS have sufficient CPU and memory to handle SMB3 which is preferred for use with any of the newer OS.

The only alternative Apple made available for Network backups is using another Mac. The original Apple Server Extension for Time Machine was ported over to standard Mac OS since High Sierra. It is not so easy or cheap to implement unless you have a suitable Mac running Big Sur or later, and a large drive hanging off it via Thunderbolt or USB.

So a NAS is now the best solution, if you insist on Network backups.

Synology are recommended for best compatibility.

You can get a dual bay cheap one .. (single bay restrict you but will work) even second hand will be adequate to the task. Nor do you need to fill it. One big disk will be fine for backups. Only if you fill it up do you need to get another disk.

Note the format of the drive used on the NAS is not a problem. Or even USB formatted HFS+ plugged into Time Capsule or any other router or suitable format. Time Machine creates a Sparsebundle that is a virtual drive, and it will be formatted APFS.

The only setup where you can backup to APFS formatted drive over a network is using a second Mac as Time Machine target. And Time Machine will still create a Sparsebundle on the drive in APFS format. That is just how TM works.

The advantage of using HFS+ is the Mac can still read and write to it.. so if something goes wrong you can still plug the drive into the Mac to read the backup.