Each of these grids is
a common logic puzzle genre. These genres are, in order:
Hidato; Str8ts; Battleships; Sudoku
Kakurasu; Skyscrapers; Minesweeper; Stars and Arrows
Tapa; Light and Shadow; Nurikabe; Fillomino
Solutions are below:

(Puzzles 2, 5, 6, and 7 were solved by Reinier.)
For the next step:
Each of the grids is a different color. (The grids on the right look black, but they are very dark shades of red, green, and blue.)
These colors are hexadecimal 88
, 44
, 22
, and 11
in one of the channels, and 0 in the other two.
The text says "get to the heart of everything... all that is left is a single color". In all of the grids, the center cell is unclued; we can use the top right guide to convert the solutions to each puzzle to "shaded" or "unshaded", and then "add" the shaded colors together.
#000000 + #440000 + #220000 + #000000
+ #000000 + #000000 + #002200 + #001100
+ #000011 + #000044 + #000022 + #000011
... = 663399
This is a color that has the name "rebeccapurple" in the CSS color list; its "deeper meaning" is that it was named after Rebecca Meyer, who was a daughter of web designer Eric Meyer and who passed away at a young age due to a brain tumor.