Partial answer

Solved slitherlink:

Next, the lines are reminiscent of

an origami fold diagram. Specifically, the dashed lines are called "valley" folds, and the dot-dash lines are called "mountain" folds.

So, I tried

printing the solved slitherlink and folding along the lines, expecting a word or something to appear, but nothing is standing out to me.

Other thoughts:

I suspect that the "ouroboros" refers to the slitherlink loop itself - I think coloring the cells was the wrong direction. When I have some time I plan on adding the lines to my printed version to see if that helps.

Did the ouroboros...

...join a CULT?

First, we solve the slitherlink:

Next, the lines are reminiscent of

an origami fold diagram. Specifically, the dashed lines are called "valley" folds, and the dot-dash lines are called "mountain" folds.

The "ouroboros" seems to refer to

the slitherlink loop itself, so the edges are what's important - ignore the cell coloring (this tripped me up for a while).

So to get the final solution, we can

print the solved slitherlink and fold along the lines:

Partial answer

Solved slitherlink:

Next, the lines are reminiscent of

an origami fold diagram. Specifically, the dashed lines are called "valley" folds, and the dot-dash lines are called "mountain" folds.

So, I tried

printing the solved slitherlink and folding along the lines, but I'm not sure where to go from here.

Partial answer

Solved slitherlink:

Next, the lines are reminiscent of

an origami fold diagram. Specifically, the dashed lines are called "valley" folds, and the dot-dash lines are called "mountain" folds.

So, I tried

printing the solved slitherlink and folding along the lines, expecting a word or something to appear, but nothing is standing out to me.

Other thoughts:

I suspect that the "ouroboros" refers to the slitherlink loop itself - I think coloring the cells was the wrong direction. When I have some time I plan on adding the lines to my printed version to see if that helps.