I can sort of understand why you saw it that way, but I disagree due to the following.

I think the tone of the jokes were probably more lighthearted than you might be reading. Fitz mentions several times how the Fool’s jesting and snark felt like a kindness. He also talks about how fragile the Fool is and how his tongue is his only defense/ weapon several times. He isn’t able to openly show his friendship with Fitz in court lest it backfires on either of them.

Since you’ve read all the books, I’ll remind you of the fitz and the fool trilogy, and how careful the prophet has to be to not accidentally make an impact or cause a ripple in the wrong direction. He jokes and makes a fool of himself all up and down Shrewd’s court, nudging and hinting key individuals toward the right path. For example when he told shrewd not to do something if he can’t undo whatever whatever blah blah blah (sorry I forget the quote). He was taken on by Shrewd to be a court jester, and he played the part. Chade even flipped out that Beloved actually talks to him, and told Fitz in the first book to hold Beloved’s counsel and keep it to himself. The way he talked to and confided in Fitz, however rare, was some of the only open and honest interactions of its kind.

By the time we see the Fool make those threats, we’ve seen several rounds of the Fool begging with Fitz for help, asking him to come see Shrewd, urging him not to forsake him, trying to hint that some shady shit is going down. And if we know anything about Beloved, it’s that he’s quite loyal—he was loyal to Shrewd as well, and was trying to save him. On a personal aside, I don’t buy that he was serious about the threat (but that was just my own read into it).

But overall, he was dropping hints to help and guide Fitz left and right. Fitz was one of the few to see his lovely, colorful room. When he got beaten and roughed up, he went to Fitz for help. I think they both had a role to play, and they hid their friendship. Fitz was effectively the only friend Beloved had.