I do think Tesla will be gradually lowering the price of the Model S. They have to do it slowly or current owners would howl.
The Model S is larger with a better cargo space, but the Model Y will probably have cargo volume close to the Model S. And other manufacturers get away with such huge price gaps between cars with smaller differences than the 3 and S, but there is no car maker in the world with more attention focused on them than Tesla.
The attention is a two edged sword. They don't need to advertise and their stock price is incredible, but they also gets tons of negative press over every hiccup and the price gap between the Model 3 and S will likely be talked about quite a bit as the Model 3 starts getting out there.
Where it counts, I do think the Model S interior is better than the Model 3. It has an instrument cluster behind the steering wheel that can be customized to some extent. It has more useful interior space for hauling stuff with the hatch as well as being somewhat roomier except in headroom. The Model 3 has most pockets for stuff, coat hooks, and is overall a newer design. That's going to draw attention.
The Model S will need to get an interior that picks up the advantages of the Model 3's design and makes it look even better to keep up sales. The Model S will continue to have a performance edge and it will likely get a range boost as soon as they are sure 2170 production can meet Model 3 needs and then some, but it's going to look overpriced for what you get until there is a refresh.