Progress in Story mode is marked by two metrics, which both come from completing levels. It makes completing levels feel more rewarding at a low development cost.
The objective given to motivate the player to play levels is to rebuild princess Peach’s castle, room by room. This gives clear visual progress steps in addition to the completion percentage displayed in the UI. The player is also given simple choices over which part to build first.
Starting construction on a part of the building costs coins. After construction has started, it finishes once the player has completed a number of levels (marked by hammer icons). While Mario is collecting coins, the Toad workers are making progress. When you come back from a level, you get to see progress in all on-going constructions, the completion percentage going up, and coins adding up.
Completing a level makes the player progress in two ways: making progress on current works, and stocking on coins for the next available parts, as it is more efficient to have multiple constructions in parallel. This is a nice way to give more weight to a seemingly weak progress objective.