> I've spent about 10 minutes Googling, and I'm still not sure how I backup and restore passkeys.
In the Apple ecosystem your passkey is / can be sent to your iCloud Keychain, which you can restore when you can a replacement device (and keep using on non-lost/stolen devices):
If you still have access to a device that can handle the passkeys then you can use the scan of a QR code to gain access.
If you do not have access to a device with your pass key on it then using iCloud Keychain is probably not the best service to use for your use case of an Android device. Use one of the many other services that also provide Android support and passkey support. Then you can access that service and access your passkeys.
iCloud is one of many. Bitwarden and 1Password will both support passkeys, both have Android support.