Double Dipping

We are presented with a grid with some numbers in some cells. The grid can be solved as two different logic puzzles, clued by the flavor text: Tapa and Choco Banana. The solutions for both grids are below:

After completing both logic puzzles, we can overlap the grids to find where the cells are the same color or are different colors, and then place this over the letter grid.

We get the following overlap (black means both cells were black, gray means one cell was white and the other black, and white means both cells were white):

The “AND/NOR” in the flavor text implies that the answer will be related to cells that are the same, so we overlap the ANDed and NORed grid over the lettered grid. Taking the ANDed (black) cells we get ANSWERISHANGBACK, and taking the NORed (white) cells, we get DENEBSCONSTELLATION. As a check, the gray letters also spell TAKE THE OVERLAPS SEPARATE COLORS. Finally, we can get the answer HANG BACK from the AND (black) cluephrase and the answer CYGNUS from NOR (white) cluephrase.

Authors' Notes

TIL Tapa and Choco Banana clues are not very complementary to each other (which is why the Tapa ended up being much easier than the Choco Banana ;-;). Otherwise, dopples (2-in-1 puzzles) are always super cool and this was very fun to write!

My favorite trick for solving Choco Bananas (I promise it's useful) is "if the cell is not shaded, then it must be unshaded".

Appendix

Tapa

Here's a possible solve path for the Tapa (grays are unknowns):

A break-in is the 8 in the top left corner (all the cells around it must be shaded because there are only 8 neighboring cells around the 8), and we can deduce the following just by looking at the numerical constraints.

Tapa also has a rule where no 2x2 region can be shaded, which allows us to figure out the 7 and then all the 5 clues.

Finally, we can figure out the 4 clues by using the "no 2x2 region can be shaded" rule to get the final solution.

Choco Banana

Here's a possible solve path for the Choco Banana (grays are unknowns):

The 7 clue cannot be shaded: it can't be vertical because other non-7 clues would be in the same region as the 7 if it were shaded, and it can't be horizontal because the 2 and the 4 in the row below would become part of the same region. We can apply similar logic to deduce that the 5's all must be unshaded as well.

The 6 clue is unshaded. None of the 6 potential 2x3 configurations work because they either result in a 6 sharing a region with a 2 or result in 7 shaded cells. None of the 6 potential 3x2 configurations work because they either result in the 6 sharing a region with a 2, the 8 sharing a region with the 4, or the 5 sharing a region with the 7.

Looking at the top 4 on the rightmost column, we realize there is only one possible configuration. If it is unshaded, then it must look like one of the following in order to avoid making different numbers be part of the same region (e.g. 4 & 5, 4 & 7):

But all of these result in immediate breakages.

Next, that same top 4 in the rightmost column cannot be a 2x2 shaded region because the 5 and 7 will be in the same region. So it must be a 1x4. The top 2 1x4 options also force the 5 to be connected with the 7, so the correct placement in the following grid connects both of the 4's in the same shaded region:

By using similar logic (avoid making two different numbers share the same region) and keeping in mind that unshaded cells cannot be rectangles (and that shaded cells must be rectangles), we get the resulting grid:

Next, we realize the 2 must have the shaded cell above it since the 6 would have too many cells otherwise. We can fill in more cells as a result of that too:

Note that the 5's cannot connect to the region of two unshaded cells to the left or there will be more than 5 unshaded cells. Then, we determine the 4 is shaded and complete the puzzle.