That’s part of the rationale for homomorphic encryption, even if the device performing the operations is completely compromised it never has access to the unencrypted data, so given a theoretical perfect HE system your data would still be safe.

I’m off to read this paper S I don’t understand how they are using a side channel to extract information that the operating device theoretically shouldn’t have. If there’s a measurable power usage difference over the operations that implies that the encrypted bits do leak information about what is encrypted.