My questions here are focused on $D$-dimensional topological quantum field theories (TQFTs) which are unitary and which have finite dimensional Hilbert space on a closed spatial manifold $M^{d-1}$. Say the partition function $$Z(M^{d-1} \times S^1)=\dim \mathcal{H}$$ is finite. The spacetime $M^{d-1} \times S^1$ can be viewed as a closed spatial manifold $M^{d-1}$ and a compact time.

We know that there are a large classes of 3-dimensional (3d) TQFT defined on a spacetime 3-manifold. Many of them are some version of Chern-Simons TQFT. Some of them can defined on any closed manifold, other TQFTs require to have the spin-manifold to be defined. For example, even for the Chern-Simons thoery, we have the $3d$ spin Chern-Simons theory requiring the spin-manifold.

My question:

What are some examples of 4d TQFT with or without requiring spin structure, say the $4d$ spin-manifold?There are a large classes of TQFTs described by twisted discrete gauge theories, say the Dijkgraaf-Witten theory.What are other 4d TQFT with or without requiring spin structure / spin-manifold?Do we have the continuous Lagrangian formulation or the lattice formulations of the theories?