Version: "spoornpink-3.3"
--> "spoornpacks-4.2-1.18.2"

The barrel recipe is overriding all barrel recipes, causing every wood type to craft Pink Blossom Barrel.

Example images:

This is expected behavior. The Barrel recipe is supposed to use the #minecraft:planks tag and #minecraft:slabs. This is even the behavior of vanilla barrel recipes:

Vanilla:

{
  "type": "minecraft:crafting_shaped",
  "pattern": [
    "PSP",
    "P P",
    "PSP"
  ],
  "key": {
    "P": {
      "tag": "minecraft:planks"
    },
    "S": {
      "tag": "minecraft:wooden_slabs"
    }
  },
  "result": {
    "item": "minecraft:barrel"
  }
}

SpoornPink:

{
  "type" : "minecraft:crafting_shaped",
  "pattern" : [
    "PSP",
    "P P",
    "PSP"
  ],
  "key" : {
    "P" : {
      "tag" : "minecraft:planks"
    },
    "S" : {
      "tag" : "minecraft:wooden_slabs"
    }
  },
  "result" : {
    "item" : "spoornpink:pink_blossom_barrel"
  }
}

You'll probably find this happening with other mods' recipes as any recipe that uses tags can "conflict". I'd recommend using the Polymorph mod which adds a button letting you choose exactly which recipe you want to craft: https://www.curseforge.com/minecraft/mc-mods/polymorph-fabric

If I instead changed the Pink Blossom Barrel to use Pink Blossom Planks/Slabs only, the vanilla recipe may override my recipe.

I think you find this wouldn't be the case and should be changed so that it does indeed use your pink planks/slabs.