This is a fantastic puzzle! Incredibly difficult, but with a really nice solution path. I have no idea how you managed to come up with this!
How to solve:
(This took me about 7 hours so my memory of early logic is fairly rusty, but I have explained as best I can)
The threes in the middle must be a 1/2, 2/1and 3 set, which means the 4s must be 4s and not a sum. The 6 can then also only be a 6, as it cant be a 5/1 as there is a 1 in the right hand grid from one of the 3s. The 9s must be a 5/4 and a 9, and the rest of the row can be filled with notations.
Top right cannot be a 3, or else there is no room for a 3 in the bottom right area which lets us place the 1, 2, 2 and 3 top right. The 6 bottom right then can only be a 4/2 pair.
The two 5s in the middle row must be 1/4 and 5, and this allows the 2 6s to also be resolved. The rest of the middle row can be filled with notation. The 7 bottom right must be a 7 as it cannot be anything else.
The pair of 1/2s in one of the rows means that the 6 top left of the central box must be 4/2. The 8 next to the 6 means that the 7/8 pairs in one of the bottom rows can be resolved. More can be placed in the penultimate row by looking at the combinations of the 3 5s.
The 9 in the left column cannot be a 5/4, or else there would be two 4s on the right hand grid, so is a 9. The 4s can be resolved, as can a lot of the left hand column. More numbers can be placed in the right hand column.
Looking at the 1s and 2s in the right hand grid, nearly all of them can be placed. The right hand grid can have some numbers resolved which allow us to place a 3 and a 5 on the right.
The newly placed 3 and 5 allow us to complete the middle column easily from here. After this, it is relatively easy to complete the left hand grid.
Moving onto the right, we know we have all the information needed, so we can solve this normally. This is mostly a process of looking at where each number can go in each row/column/box, and searching for hidden singles. We can get pretty far just by doing this:
And finally, cleaning up the right hand grid and entering the last few numbers we can finish the puzzle: