Even the condition that you have a collection of Lagrangians which are categorically orthogonal and each with $ HF^*(L)=H^*(L) $ as an $ A_{\infty} $ algebra is unreasonable: There could a priori be symplectic manifolds with such Fukaya categories, but at the present state of knowledge, it is unlikely that we would be able to prove it since all methods for proving that a certain collection of Lagrangians generate the Fukaya category ultimately pass through a split-generation result for the diagonal (even the one used in Seidel's book can be interpreted in that language). On the other hand, the category you describe does not have such a resolution (you can see this by noting its Hochschild cohomology is a direct sum of homologies of free loop spaces and hence is of finite homological dimension).

Even the condition that you have a collection of Lagrangians which are categorically orthogonal and each with $HF^\ast(L)=H^\ast(L)$ as an $A_{\infty}$ algebra is unreasonable: There could a priori be symplectic manifolds with such Fukaya categories, but at the present state of knowledge, it is unlikely that we would be able to prove it since all methods for proving that a certain collection of Lagrangians generate the Fukaya category ultimately pass through a split-generation result for the diagonal (even the one used in Seidel's book can be interpreted in that language). On the other hand, the category you describe does not have such a resolution (you can see this by noting its Hochschild cohomology is a direct sum of homologies of free loop spaces and hence is of finite homological dimension).