I give up. You are conflating pumped storage with tidal power again.
Tidal power can store the energy until it is required (at a reduced capacity). The power delivery can be planned around the other generators due to its extremely high availability and certainty, and its able to rapidly ramp up/down to closely follow demand cycles.
Or the additional costs to make it pumped are very low if its designed in when built. Then you can not only store the energy from the tidal power but also excess energy from other sources.
Either way tidal energy is able to store energy and deliver it when its needed most, or it can run as a predictable but intermittent generator. Market forces will determine which of these modes it would operate in but the existing data suggest that it would be more profitable as a peaking plant, and more profitable again if pumped.