Unlike all other game modes, in Peaceful mode you can't die. The board is 15x17, this means the worst case apple is max 16 blocks away, where you have to run half the board for "up-down" as well as "left-right". Imagine as if you are in the middle at all times, the shortest path to any apple will be 16 blocks (max) or less. 16 blocks take around 2.435 seconds.

As for how apples spawn, they can only spawn where the snake isn't filling up the block. They spawn 100% random, as confirmed by the developer (CLTincknell). In peaceful however there's something extra, when you reach high numbers, for some reason, apples tend to spawn less in the right side of the board - looking at all the 252 runs you can see this happen across all of them. Where even if there's 2-4 empty columns in the right ready for an apple to spawn there after you eat one, it never does. CLTincknell says that apple spawning logic in all modes is uniformly random - so this may be a bug. Update: turns out this was a bug, and it's now fixed, as CLTincknell said: "The logic for finding an unoccupied cell for the new apple wasn't taking Pacifist into account and was assuming that the snake was occupying a unique cell for each of it's body segments"

Regardless, the optimal strategy for any Peaceful category of apples is to aim for the shortest path to any new apple. Another helpful tip is after you eat an apple, if possible, go for an empty space where another one might spawn. When you are about to go over yourself - that's a block where an apple won't spawn and going over it will cost time, this is especially helpful in high apple categories, as empty blocks become less available, aiming for them preemptively will save time.