You're getting it backwards though. You are right that the whole point of an HSM is to not leak secrets when connected to a compromised computer. However there's nothing wrong with a HSM device that can be initialized with a "seed" of your liking, as long as that initialization step is done in a fully offline / airgapped way.
Ledger (whose CEO was, before creating Ledger), one of the member of the team working on the FIDO specs, make a "hardware wallet" for cryptocurrencies that can run a FIDO app. And it's totally possible to initialize the seed of your liking for your U2F device.
Now I did test this a while ago (out of curiosity) and it all working but I'm not really using it atm: I don't know where it's at regarding the latest FIDO2 specs.
But the point is: what GP asked for can totally be done.
I understand some may want to move the goalpost and say: "ok but then the problem now is not losing your piece of paper where you wrote that seed". But that is another topic altogether that does change nothing to the fact that you can have an HSM used for U2F that can be backed up.