Continuing from dcfyj's and Kevin Cruijssen's solutions, the next step is toFirst...
... solve the Sudoku, as instructed.
Credit to dcfyj and Kevin Cruijssen for solving this step first.
The completed grid, as depicted by Kevin Cruijssen, looks like this:
Next...
... solve the 5x5 Futoshiki puzzle formed by the white squares and the red-circle inequality symbols between them.
The finished grid looks like this:
NextFinally...
... we apply the color-coded arithmetic symbols to each row and column. There are four symbols in each row/column (plus an equals sign), which fits perfectly!
Standard order of operations apply. The completed grid reveals our answer.
The new puzzle type's name is...
SUDOSHIKI.
Great construction, Stiv!