You've learned broken profile DP. You know how to represent which cells protrude from one column to the next as a bitmask, precompute valid transitions, and propagate counts forward. Good job. You solved three tiling problems: general grid with dominoes, grid with its recurrence, and grid with trominoes.
You saw how profiles collapse into recurrences when width is fixed. For practice, solve more tiling problems with different constraints: grids with obstacles, different tile shapes, or grids where you want to find the largest some value instead of counting tilings.