No, fireplaces, pellet stoves and wood stoves are not eligible for ENERGY STAR certification.
For information on how to find the most energy efficient biomass/wood stoves, please visit this EPA webpage: https://www.epa.gov/compliance/list-epa-certified-wood-stoves. The list of EPA certified wood and pellet stoves contains efficiencies for most, but not all, wood and pellet stoves. It is updated multiple times a year and all stoves should have listed efficiencies by May 2020.
The vast majority of American homes that heat with biomass use either cordwood or wood pellets. However, the technical definition of "biomass fuel" includes agricultural crops and trees, wood and wood waste and residues (including wood pellets), plants (including acquating plants), grasses, residues, and fibers.
The tax credit for biomass stoves expired Dec 31, 2017.