What does Precision Movement/Holding L2 do as a goaltender?

It's best to always have precision movement on as a goalie as they will take small strides to stay in position instead of moving drastically from side to side..  Just make sure it's on in the goalie controls.

It's a holdover from previous controls. In prior years, goalies could hold L2/LT (or set precision movement to default) to have your goalie make slower, more precise movements. If you released L2/LT, your goalie would make larger, quicker movements called t-pushes. Unfortunately, the t-push skating animations were clunky and tedious to use, so most goalies simply played with precision movement as the default (you wouldn't need to hold L2/LT.)

This changed in NHL 24 with the introduction of the Instinct mechanic which required the player to hold L2/LT to activate the mechanic and use RS to aim. As a consequence, the precision movement was simply made the default movement and t-pushes were done away with. The feedback you're seeing regarding precision movement is simply a vestige of an extinct control option.