No clue whether this is a bug or on purpose, but I thought Id put it in here just in case, and to get confirmation.
The "Breed a foal with double recessive mushroom genes" and "Capture 3 horses with double recessive mushroom genes" both only count horses after a gene test, rather than when they're actually bred or captured. They can also be backdated, so I can test a horse I caught/bred before I got the quest in order to complete it (although I beg for this to stay if the gene test requirement is here to stay 🤣). Since thats not in-line with the other gene-related quests I wasn't sure if its an oversight.
The breed a premium mushroom quest is completing without a gene test absolutely fine, and I haven't noticed or heard about any issues with the wild bay ones.