I'm not a fan. But what Anthropic SHOULD have done is use plain ol' SSO. Google, GitHub, Microsoft, etc. logins with the option to do this magic link stuff. The third party auth providers would use passkeys at the user's discretion.
I store passkeys and totps in 1Password. I know it means there's no hardware protection of the secure element, but in return they're trivially synced across my devices.
I feel this tradeoff is worth it to me; certainly it is no worse than email or SMS as the second factor.