Linear combination IOP for SNARK registers
The prover does not send another oracle as you suggest in #3. Rather, both parties invoke the FRI protocol for the function that is the random linear combination (random coefficients selected in #2). Now, every query to the function you refer to in #3 is answered by querying all oracles #1 and computing the linear combination #2 (which is something the verifier does). Thus, the soundness error for this function is 0 and there's perfect consistency, by construction.