Future far-infrared astronomy missions will need large arrays of detectors with exceptionally low noise-equivalent power (NEP), with some mission concepts calling for thousands of detectors with NEPs below a few $times 10^{-20}$ W/$sqrt{mathrm{Hz}}$. Though much progress has been made toward meeting this goal, such detector systems do not exist today. In this work, we present a device that offers a compelling path forward: the longitudinal proximity effect (LoPE) transition-edge sensor (TES). With a chemically-stable and mechanically-robust architecture, the LoPE TES we designed, fabricated, and characterized also exhibits unprecedented sensitivity, with a measured electrical NEP of $8 times 10^{-22}$ W/$sqrt{mathrm{Hz}}$. This represents a >100x advancement of the state-of-the-art, pushing TES detectors into the regime where they may be employed the achieve to goals of even the most ambitious large and cold future space instruments.