agree with both above as plausible.
I highly recommend not operating that machine any further than necessary to diag the failure and locate the source of that broken part.
full function test may reveal the culprit. it's difficult to believe something that size breaking isn't preventing or at least inhibiting a major function in your machine. especially considering the amount of force exerted on it to break. since you haven't noticed a loss of function performance, might be something you seldom or never use that was accidentally engaged while mowing and you didn't notice movement or sound.
my first thought is it looks like a spool valve linkage or toggle, or possibly the spring bias or detent side of the spool.
I also recall a 140k grader that one of my mechanics found a big chunk of metal during a fluid change, fell out of the drain plug though. turned out to be a solenoid actuated neutral lock that worked in concert with the parking brake system. after contacting quinn we discovered there was a pip for it and the dealer repaired that machine and their field techs retrofitted the other machines.
as mentioned above, a thorough scan of the internal hydraulic system and final drive drawings should reveal something similar for some clues.
and once you figure out what it is and where it came from, don't forget to inspect for collateral damage to whatever components were gnawing on it.
good luck!
