Switch to a non-open protocol or walled garden, preferably controlled by a large and litigious organization that guards its content jealously. They'll probably still sell access to their data to LLM trainers but not necessarily Facebook.
Reddit, for example, may fit the bill. IIRC they sell their data to OpenAI for training, so there might be exclusivity deals intended to keep Facebook out.
I don't see any way to "mitigate" this while still using the ActivityPub protocol. This isn't about a bot posting on the Fediverse, it's about reading the Fediverse. If you want to prevent that then you're probably talking about some form of DRM or a walled garden.
Post and repeatedly endorse generally inoffensive content that for some reason violates Facebook’s ToS, such as the comic book cover of Captain America punching Hitler or the Led Zeppelin album “Houses of the Holy”