The CONNIE experiment uses high-resistivity silicon CCDs with the aim of detecting the coherent elastic scattering (CE$\nu$NS) of reactor antineutrinos with silicon nuclei at the Angra-2 reactor. It was recently upgraded with two Skipper-CCDs, increasing the sensitivity reach down to a record 15 eV, and becoming the first experiment to employ Skipper-CCDs for reactor neutrino detection. We report on the new results from 300 days of 2021-2022 data with a total exposure of 18.4 g-days. The difference between the reactor-on and off rates shows no excess and yields upper limits at 95% CL on CE$\nu$NS. We also present the results of three searches for physics beyond the Standard Model to illustrate the potential of Skipper-CCDs: a limit on new neutrino interactions in simplified models with light vector mediators, a dark-matter search by diurnal modulation yielding limits on DM-electron scattering, and a search for relativistic millicharged particles produced by reactors. Finally, the prospects for increasing the detector mass are discussed.