Answer: INTONE
Kevin Zhou (Kaz)

Despite what the puzzle title says, we should solve the logic puzzles. Here are solution videos for the three logic puzzles:

Yajilin Video
Heyawake Video
Shakashaka Video

Now, we use the first three bullet points of the flavortext, as well as the grid of characters, to extract.

Logic puzzle Extraction grid Explanation Extracted letters
Take the letters corresponding
to the shaded squares.
Then, read top to bottom, left to right.
There is a longest loop of unshaded cells.
Take the letters along this loop.
Then, read along the loop.
Take the letters inside
the vertical 1x2 dominoes.
Then, read top to bottom, left to right.

We have extracted 3 new genres! Each of the original puzzles continues to work with the new genre type. Thus, we have three more logic puzzles to solve.

Note that it's possible to create the Islands and Akari just by changing the genre name in the link. However, for Castle Wall, we must manually make the puzzle. Here are links to the "second layer" of logic puzzles:

Castle Wall Player
Islands Player
Akari Player

Here are solution videos:

Castle Wall Video
Islands Video
Akari Video

We use the last three bullet points of the flavortext. This time, we do not use the grid of characters, but look at the big picture. From each solved grid, we extract two letters, which is clued by the ??'s in the original puzzle image.

Logic puzzle Extraction explanation
The loop draws a shape of the US state of Indiana.
The abbreviation of Indiana is IN.
The islands of size 7 and 16 form the letters TO.
The lightbulbs near the middle form an arrow pointing northeast.
An abbreviation of northeast is NE.

Putting the extracted pairs of letters together, we get the final answer, INTONE.

Author's Notes

More seriously: This puzzle is a parody of the STOP DOING MATH meme. Constructing this puzzle took a very long time! There were dozens of failed attempts to create puzzles that are valid in two genres. Especially for the middle puzzle, I spent at least 20+ hours attempting to get a Mochikoro/Nuribou puzzle. I came extremely close many times without success. In the final product, the Heyawake/Islands is not entirely "clean" (because of the one given shaded cell), but I was just glad something nearly worked.

I really wanted to say "We had a tool for that: it was called BIFURCATION" in the flavortext, but instead it lives here in the author's notes.