Variable X-ray reverberation in the rapidly accreting AGN Ark 564: the response of the soft excess to the changing geometry of the inner accretion flow

X-ray reverberation, which exploits the time delays between variability in different energy bands as a function of Fourier frequency, probes the structure of the inner accretion disks and X-ray coronae of active galactic nuclei. We present a systematic X-ray spectroscopic and reverberation study of the high-Eddington-ratio narrow-line Seyfert 1 galaxy Ark 564, using over 900 ks of \textit{XMM-Newton} and \textit{NuSTAR} observations spanning 13 years. The time-averaged spectra can be well described by the a model consisting of a coronal continuum, relativistic disk reflection, warm Comptonization, and three warm absorbers. Leveraging the high X-ray brightness of Ark 564, we are able to resolve the time evolution of the spectra and contemporaneous reverberation lags. The soft-band lag relative to the continuum increases with the X-ray flux, while Fe K$\alpha$ lags are detected in only a subset of epochs and do not correlate with soft lags. Models based on a lamppost corona and reflection from a standard thin disk can broadly reproduce the observed lag-energy spectra of low-flux epochs; however, additional reverberation from the warm Comptonized atmosphere is required to explain the soft lags observed in high-flux epochs. A vertically puffed-up inner disk and a variable, vertically extended corona can better explain the observed evolution of the lags and covariance spectra. Our study underscores the importance of multi-epoch, multi-band analyses for a comprehensive understanding the inner accretion disk and corona.