Star formation timescales are key to understanding fundamental physics like feedback mechanisms, as well as the abundance of bright galaxies at $z>10$. We investigate galaxy star formation histories (SFHs) and their evolution across $z\sim3$--9 by measuring the line-to-UV ratio (\rline) and line equivalent width (EW) of \hanii\ and \oiiihb\ directly from UNCOVER/MegaScience spectro-photometry without relying on a specific SFH or nebular line modeling. Our photometric measurements recover \rline\ and EW to $<10\%$ systematic accuracy compared to spectroscopy. This allows us to construct a large mass- (and flux-) complete sample and quantitatively examine how \rline\ evolves with redshift and stellar mass. We find that the intrinsic scatter in \rline\ does not significantly evolve with redshift across $3<z<7$, though it may increase at $z\gtrsim8$. We build population-level toy models using \texttt{fsps} to help interpret our observations, and find that scatter in \rline\ primarily reflects the amplitude of SFH fluctuations; this implies that our observed lack of evolution in the scatter of \rline\ is due to similar star formation burstiness from $z\sim3$ to $z\sim7$. Our observations are best reproduced by a set of SFHs with rising, long-duration, and large-amplitude bursts. Finally, we demonstrate that the toy model that best describes our $z\sim6$ data can boost UV brightness by up to $\Delta M_{\rm UV}\sim-2.0\,{\rm mag}$ compared with a 200\,Myr constant SFH, and naturally produces a large number of galaxies at $z>10$. This suggests that no significant evolution in star formation burstiness is required to explain the abundance of UV-bright galaxies at high redshift.
We present near- and mid-infrared spectra of eight Low-Luminosity Active Galactic Nuclei (LLAGN), spanning nearly four orders of magnitude in black hole mass and Eddington ratio, obtained with JWST/NIRSpec and MIRI as part of the ReveaLLAGN program along with identical archival data of Cen A. The high spatial resolution of JWST cleanly separates AGN emission from host-galaxy contamination, enabling detections of high-ionization potential lines more than an order of magnitude fainter than previously measured. Emission-line diagnostics reveal a transition at log($L_{bol}/L_{Edd}$) ~ -3.5, where the spectral energy distribution becomes increasingly deficient in ultraviolet photons. We find that rotational H$_2$ excitation temperatures are elevated (~500 K higher) compared to both higher-luminosity AGN and star-forming galaxies, while the H$_2$(0-0)S(3)/PAH$_{11.3 \mu m}$ ratios are consistent with those observed in the AGN population. We discuss the possible roles of outflows, jets, and X-ray dominated regions in shaping the interstellar medium surrounding LLAGN. Silicate emission at ~10 $\mu$m, localized to the nuclear region, is detected in most ReveaLLAGN targets. This dataset offers the first comprehensive JWST-based characterization of infrared emission lines in the nuclear regions of LLAGN.