The classical obstruction and the surviving quantum mouth

This is standard teleportation, not recovery from classical data alone Teleportation. The quantum output is carried by $E$, and the Bell resource and communication are part of the contract.

In the main Haar model, entering $P_k$ and retaining $E$ produces a hybrid interface. We neither assume that it remains recoverable nor apply the record-only bound to it without further analysis. Its Shannon record entropy is still append-only and nondecreasing.