SSD time machine backup/ router compatibility. Is there a router that reads APFS?

Does the SSD connect using Thunderbolt or using USB?

Very few routers will support Time Machine backups at the USB port on the router. Among the few that will are Synology and the upper end Asus routers. There may be more, but I have not found them.

Look over the technical specifications of any router that you might be considering to make sure that the router will support Time Machine backups. If you do not see this listed, you have to conclude that Time Machine backups are not supported.

I know of no router that will support a hard drive that is formatted as APFS when the HD is connected to the USB port on the router.

The SSD will need to be formatted as Mac OS Extended (Journaled) if you want to connect it to a router that does support Time Machine backups at the USB port.

To add a bit to Bob's excellent comments ...

... for a Synology NAS, it does have the option to connect an external USB drive. The NAS could then be configured to make backups to that drive with the source being the NAS' internal drive(s).

For example, I use my Synology NAS for Time Machine backups. I have been doing so since Apple decided to get out of the networking hardware business back in early 2018. I have a (in my case) a WD My Passport drive connected to this NAS. I then have the NAS configured to copy the Time Machine backup set to this external drive periodically for added "insurance."

I intend the SSD to be connected to the router via USB. But if that's not a feasible option, what would be the best way to have a network backup, like what the old Time Machine used to do?

OK, thanks for the clarification on that. The critical piece of the puzzle is that the router must support Time Machine backups at the USB port.

Unfortunately though, the fact that router might have a USB port does not necessarily mean that Time Machine backups will be supported. You will have to verify that Time Machine will be supported on any router that you are considering.

This is the next best thing to a Time Capsule, which included a built in hard drive designed to store Time Machine backups. A USB hard drive that is connected to an AirPort Extreme will work as well, so that might be an option. There are plenty of AirPort Extremes available on eBay.

Otherwise, the only way to set up your SSD as a "network" drive would be to connect it to Mac desktop and try to work through a complicated setup. This used to work on older Mac operating systems, but I"m not sure about Ventura.

Probably the best way to set up a network drive is go with a Network Attached Storage (NAS) device from Synology, but the expense is substantial. You might want to poke around on the Synology website to get a feel for things.

I want to have a physical backup drive, so for example I can take it with me when I go on holidays, incase I get robbed/ the house burns down etc. I just assumed it would be a portable hard drive connected to a router.

Understood. A USB drive connected to a Time Machine compatible router would probably be the best way to go in that regard.