I think you nailed the effect, just have to combine the two: both forms of inflation could occur. First through prices as consumer goods become more expensive

I think you nailed the effect, just have to combine the two: both forms of inflation could occur. First through prices as consumer goods become more expensive, then later through increased wages to compensate as well as capture some of the excess returns capital earns. In the textbook version, we'd end up in the same spot.