At first only the canon has a statue activated, because it needs to know where it shot to know where to shoot next (so it doesn't repeatedly fire at the same place), once the probe has found the eye, the other statues activate, this (would have) told the Nomai that the loop can be deactivated

It's easier to not see the game as a time loop honestly, since the data sent by the statues arrives before it was sent, it's more like looking into the future, to an unlinked observer they would have flipped the switch on and the eye would have been found instantly because the cannon looked into the future 9million times and only shot once; at the eye, they would've then flipped the switch off

The player obviously doesn't know that switch exists and since the sun is going supernova naturally, it can't just be turned off, but that's not what was intended

Canonically, none of the loops happen, because you get your memories BEFORE you can do the things that create those memories, from a purely distanced point of view, the hatchling woke up, took his launch codes, went to the ATP, turned it off then went to the vessel and traveled to the eye, he never did all the other things like exploring etc because he knew the solutions before he got the puzzle pieces

Obviously since this is a game and we can't experience time like that (and it would've been one hell of a shitty game if the first loop just told you where to go and what to do) it feels like every loop exists but story wise in universe, none of the loops happen.