I am not english native. Is "The W" a synonym for "A Win", described as a positive outcome after a contest? Is there more nuance or context than that?

Yes, but it's often just "a W" or simply "W" in response to something good or seen as a "win."

There is also the same thing with L for loss/loser. "that's an L take", "L [person]", "take the L here", etc.

They are pretty straightforward in their meaning, basically what you described. I believe it comes from sports but they are used for any good or bad outcome regardless of whether it was a contest.

I think it's from people reporting sports statistics for a player or team as "W:5 L:7" meaning "five wins and seven losses".

https://knowyourmeme.com/memes/l-and-w-slang