Gaiotto Conjecture for Repq(F(4))

This paper is a part of the series proving the Gaiotto conjecture for basic classical quantum supergroups. The previous part arXiv:2107.02653 [math.RT] , arXiv:2306.09556 [math.RT], proved the Gaiotto conjecture for the general linear quantum supergroups Uq(gl(N|M)). Here we deal with the exceptional quantum supergroup Uq(f(4)).