Microcombs generated in optical microresonators are widely regarded as promising light sources for next-generation communication systems, but the optical power available per comb line has so far fallen short of practical requirements. Here we introduce an integrated Fabry-Pérot microresonator platform that overcomes fundamental dispersion-engineering constraints and enables bright soliton microcombs with unprecedented power per line. The resonator is defined by chirped Bragg gratings that provide exceptionally large anomalous group-velocity dispersion, allowing more than ten comb lines to reach the milliwatt level. These combs can be used directly in coherent communication systems without additional amplification, achieving an aggregate data rate of 2 Tb/s. Once integrated, our high-power soliton microcombs could be instantly ready for communications as well as a broad range of practical comb-based applications.