Five ways.
A sharper perspective.

Use nine irregular regions instead of square boxes. Every row, column and outlined region must contain each colour once.

Diagonal adds the two highlighted main diagonals to the standard Sudoku rules. Anti-knight prevents equal colours a chess-knight move apart: two squares one way, one square sideways.

Loops asks you to draw exactly one continuous loop with no branches, satisfying the cell clues. Bridges asks you to connect all islands with one or two non-crossing horizontal or vertical bridges, matching each island number.

In Chroma, placing an incorrect full colour costs a life. Notes do not. In Loops and Bridges, editing is free; pressing Check on an incorrect board costs one life. Three mistakes lock the challenge until you retry.