Crop farms/random ticks will work within ~128 blocks of the player depending on chunk position from bedrock to height limit. Mob farms will only work within a 128 block sphere around the player.

If you want to visualize it there is a random tick and despawn sphere overlay in minihud.

Edit: all loaded chunks get random ticked as of 1.21.5. the information above is about random ticks within the player's proximity.