This is true for any [citation needed] hardware security module. The interface allows to store/generate secrets and request cryptographic operations (encryption, signing, etc). Aside from physically tampering with the chip to access bits in raw silicon there is no way for the secret itself to leave the chip. Software security modules behave the same way, with the exception that one does have software access to the backing encrypted storage.
Yubikeys can be backed up, using what they call export under wrap. It requires you initially created the key with exportable flag. The idea is you do this on first use to create an encrypted backup and then instantly remove the exportable flag from the key you carry around day to day.
As others already noted, having more than one key is a good idea anyway. If you are really serious, use ssh certificates so you don’t have to update every server with new keys. Just sign them with the root CA.
Yes, you can’t extract it, the Secure Enclave can just create a key and has it to sign stuff.
You can never actually grab it or access it for backing up, so it shouldn’t be your only way of accessing a server, there should be another authorised key that you do have access to.
It depends on the setup. You can generally only ask an hsm to perform a few specific operations “encrypt this data”, “sign this data”, etc and you’re restricted to the exact formats that it supports.
Because they are generally not very configurable (their design goal is to be secure and so the less complexity the better) it’s fairly common for them to just not directly support any specific cryptographic protocol.
Given that, what you can choose to do instead is have the hsm generate a key for you, and then you use that key to wrap your specific secret - say an ssh key - then you decrypt it when you need it which requires user authentication through the hsm - use the raw key and then clear it from memory.
But if the only record of the external key is wrapped by the hsm, if the hsm loses that decryption key then you’ve lost access to the ssh (or whatever) key as well.
It's designed to make it hard, but it does crypto operations using the key so it's in there and possible to extract similarly as other tamper resistant chips have been successfully physically attacked.
