I can see why you're confused - it looks like something has changed with the Playdate SDK since the first Shift was released and the score is not updating correctly. It knows what your score is, its just not being reflected in the UI. Shift II does not appear to have this issue.
I'll get this fixed and report back here when its been updated on Itch and Catalog.
That said, in Shift each tile is worth 1 point, multiplied by your current streak.
In Shift II, each tile is worth 1 through 6 points, multiplied by your current streak. The point values for each tile type can be seen when you pause the game via the menu button.