Dark Quest II: A Wide-Coverage Neural Network Emulator of the Nonlinear Matter Power Spectrum Across Extended Cosmologies

textscDarkEmulator2 is a neural network emulator of the nonlinear matter power spectrum in a nine-dimensional w0 wa nu o CDM parameter space, developed as the emulator component of the textscDark Quest II (DQ2) program. It is trained on simulations generated with the textscGinkaku code, whose numerical implementation, accuracy tests, and post-processing pipeline are described in the companion paper. The design follows a unified strategy: in addition to the cosmological parameter vector, we supplement the neural network's inputs with three families of physically motivated auxiliary quantities -- the linear matter power spectrum, descriptors of the simulation resolution, and a low-dimensional summary of the initial Gaussian random field -- that are expected to improve generalization across the parameter space. Training a single network jointly across three simulation resolution tiers allows the emulator to exploit a small number of high-resolution simulations while retaining broad coverage from lower-resolution simulations. For a Lbox=1,hiGpc box with N=30003 particles, the emulator reproduces the simulated matter power spectrum to subpercent accuracy up to the particle Nyquist scale, kNysimeq 10,hMpci. The emulator remains accurate over the calibrated wavenumber range, while its highest-k predictions depend on the simulation resolution and shot noise. We validate the emulator on independent test suites and, through a cross-comparison with several public emulators and widely used fitting formulas, characterize the inter-model consistency and the parameter-dependent trends in their residuals.