Pretty straightforward:

While models' texture references are formatted assets/<namespace>/textures/<name>.png, particles' texture references are formatted assets/<namespace>/textures/particle/<name>.png.

The particle atlas should set the prefix to "particle/" for consistency. The current behavior is incorrect, as having the prefix is consistent with sound, model, loot table, function, tag, advancement, dimension, dimension type, structure and feature references.

Examples:

Model:

{
  "parent": "minecraft:item/generated",
  "textures": {
    "layer0": "minecraft:item/acacia_boat"
  }
}

Texture path: assets/minecraft/textures/item/acacia_boat.png

Particle:

{
  "textures": [
    "minecraft:angry"
  ]
}

Texture path: assets/minecraft/textures/particle/angry.png
Expected with this input: assets/minecraft/textures/angry.png

The fix:
Replace "prefix": "" with "prefix": "particle/" in assets/minecraft/atlases/particles.json, and replace minecraft: with minecraft:particles/ in assets/minecraft/particles/<particle>.json.