Convergence actually established that Barry was the same person pre-Crisis to post-Crisis. During his tie-in book with the Tangent Super Man, Barry was shown to be unmoored from the multiversal timeline even within the Convergence battle world, which is how he knew about the Speed Force and why Super Man had to sacrifice himself for Barry to preserve the multiverse. So Barry remembering his pre-Crisis and post-Crisis lives still fits with Convergence