  We study spectral correlations in many-body quantum mixtures of fermions,
bosons, and qubits with periodically kicked spreading and mixing of species. We
take two types of mixing, namely, Jaynes-Cummings and Rabi, respectively,
satisfying and breaking the conservation of a total number of species. We
analytically derive the generating Hamiltonians whose spectral properties
determine the spectral form factor in the leading order. We further analyze the
system-size $(L)$ scaling of Thouless time $t^*$, beyond which the spectral
form factor follows the prediction of random matrix theory. The $L$-dependence
of $t^*$ crosses over from $\log L$ to $L^2$ with an increasing Jaynes-Cummings
mixing between qubits and fermions or bosons in a finite-sized chain, and it
finally settles to $t^* \propto \mathcal{O}(L^2)$ in the thermodynamic limit
for any mixing strength. The Rabi mixing between qubits and fermions leads to
$t^*\propto \mathcal{O}(\log L)$, previously predicted for single species of
qubits or fermions without total number conservation.
