Let’s untangle those problems. I have a similar setup so I just want to share some ideas to show that you don’t need to copy keys.

If I’m traveling or I wipe my device or get a new one, I would have to add the new key to many servers as authorized keys

If you oftentimes access ssh from untrusted systems you’re kind of in a bad spot to begin with. The best thing you can have is a yubikey on a keychain. Everything else means you leak secret material (a password or a key) to a machine you don’t inherently trust.

Also, I want a key backed up in case of disaster since all of my devices are in my home most of the time

Again, something that you can easily solve with a hardware key [in a safe]. But realistically, in case of a disaster a local shell password login should be good enough?

I’d recommend you to think about what attacks are you trying to prevent by using a shared private key. I’m not saying it’s a bad concept, inherently having it in your password manager (like 1Password that even has ssh-agent support) is pretty common. The problem with just the keys is that it’s non-trivial to expire them if needed. You might be indeed better off with some web based authentication that you can access from any place which would ask you secret questions/send you a text message or do whatever 2FA you deem sufficient and mint you a short-lived certificate for ssh.

Not an answer, but I’m curious: what’s wrong with just having several ssh keys, one per device?

Local models are really good at tokenizing the text and figuring the intent in the user input. Not perfect, but much better than any possible regexps you can think of. And it’s a trivial operation you can run even on a CPU model.