First, let's take a look at the rows and columns with 0s
They must have the 1 and 9 right next to each other. We can actually determine the exact placements of the 1 and 9 for each. In C5 and R6 one side of the existing 1 is blocked. In C1 and R9 one side of the existing 9 can't have a 1 because of sudoku rules. In C8 the 9 must now go in the bottom-right 3x3 box, and there is only one way to fit a 1 near it without contradicting row clues.
I got to here with plain "This is the only place for <number> to go in this box/row/column" logic.
Let's use the top-edge clues once again!
From left to right: The 1 in C3 must go on the top, so that all of 2-8 (summing to 35) can sandwich between 1 and 9. The only way to sandwich a 4 in C4 is to sandwich a single 4, and there is only room for that to happen in one way. The 9 in C7 must be the bottom of the sandwich as below it sums to more than 6. The sandwich must use the 2 above; the only way for a sum of 6 is 2+4 so that can be placed. In C9 there is already a sum of 13 below the 9, and a 1 will finish that sandwich.
Another round of plain "This is the only place for <number> to go in this box/row/column" logic.
Now to use the left-edge clues
From top to bottom: R1 has a sum of 11 to one side of the 1 which can be safely sandwiched away. The 9 in R3 must be on the left side of the 1 to allow for a large enough sandwich, and there is only one spot that it can be placed due to sudoku logic. Both the 1 and 9 in R7 are there, and the sum of 10 can be completed as 6+4.
To wrap it all up,
The rest of the sudoku can now be completed with "This is the only place for <number> to go in this box/row/column" logic.