Observations at (sub-)millimeter wavelengths provide a valuable complementary perspective on the Sun and other stars, particularly regarding the thermal and magnetic structure, as well as the dynamics of their chromospheres and the resulting activity. While significant progress has been made in (sub-)millimeter solar observations, certain critical aspects still require diagnostic capabilities beyond those available with current observatories. In particular, simultaneous observations of the radiation continuum across an extended frequency range would enable the mapping of different atmospheric layers and, ultimately, the three-dimensional structure of the solar atmosphere. Capturing large regions of the Sun–or even the entire solar disk–with high temporal cadence would be essential for systematically identifying and tracking the temporal evolution of solar flares. Synoptic observations at higher angular resolution, such as daily maps spanning multiple years, would offer an unprecedented perspective on the solar activity cycle in this wavelength regime. Given that the Sun serves as a fundamental reference for investigating the atmospheres of active main sequence stars, utilizing the same instrument to observe both the Sun and other stars would unlock significant diagnostic potential for studying stellar activity and its implications for exoplanet habitability. The proposed Atacama Large Aperture Submillimeter Telescope (AtLAST), when equipped with a large array of detector elements to probe the radiation continuum across a broad frequency range, would be well-suited to deliver these essential observational capabilities. We present an overview of key science cases for AtLAST and considerations for the design of an instrument in comparison to potential upgrades of the Atacama Large Millimeter/submillimeter Array (ALMA), highlighting future scientific opportunities for studying solar and stellar activity.