For about a year, I've noticed that when I'm relaxed, I play chess better. But I wasn't ever able to quite figure out why, or how to get myself in that relaxed state. Now, I think I've done it, and it's stabilized my score on Lichess at around 1675 rather than 1575. That means I'm now evenly matched with opponents who'd previously have beaten me 64% of the time.
The trick is that I changed my visual relationship with the chessboard. Previously, I focused hard on the piece I was considering moving, almost as if I was the piece, and had to consider the chess board "from its point of view." If I was considering a bishop move, I'd look at the diagonals it could move along.
Now, I mostly just soft-focus on the center of the chess board, and allow my peripheral vision to extend to the edges of the board. I don't stare directly at the piece I'm moving, but rely on peripheral vision to place it correctly. By doing this, I think my system 1 can get engaged in recognizing good moves wherever they might be found.
As I do this, I notice my brain starting to scan for obvious threats and opportunities: rooks lined up diagonally, which is vulnerable to a bishop; a knight and bishop with one square between them from side to side, which is vulnerable to a pawn fork; a piece left hanging. If I don't see any, I just find sensible moves and make them without thinking about anything too hard.