When the server is the final recipient of a message sent over TLS, then yes, that is end-to-end encryption (for instance if a load balancer is not decrypting traffic in the middle). If the message's final recipient is a third party, then you are correct, an additional layer of encryption would be necessary. The TEE is the execution environment that needs access to the decrypted data to process the AI operations, therefore it is one end of the end-to-end encryption.
No need to make up hypotheticals. The server isn't the final destination for your LLM requests. The reply needs to come back to you.
This interpretation basically waters down the meaning of end-to-end encryption to the point of uselessness. You may as well just say "encryption".