I'm aware this is not a question, and this topic would be more suited to Github, but I thought it would not hurt to talk about it here too.
As of 3.2, the "Animation Looping" double arrow in the animation player node is still broken. It works in the editor's viewport, but is not saved when the game is played, or when the project/editor is shut down and reopened.
I know I can add "-loop" at the end of every animation's name that requires to loop, or I can even tell which animation I want to loop by code, but it seems silly to have a useless button in the editor, which is supposed to save some writing and allow to quickly change whether or not an animation is looping.
The problem is not new as it has been reported a few years ago already :