F1 is really tricky because there can be so many variations of the animal. I would say it would become it's own breed once all individual offspring start looking alike and are bred to a set standard.
Examples:
Labradoodles vary so much. I still see them as a designer mutt dog. I haven't seen two that looked similar. And most are still just F1 or F2s. Maybe with more time, we can see more consistency.
Bengal cats, however, I believe are their own breed now. There have been traits established as a standard that breeders keep breeding for. Cats that are ~F5 and beyond do look similar and overall have a consistent look.
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