No, the bill doesn't give official power to overturn elections.
It merely provides a way to resolution to cases where a polling place screws up and threatens voters' abilities to cast their ballots: try again, and be more professional this time.
It's really not as sensational as these articles are trying to sound.
https://capitol.texas.gov/tlodocs/88R/billtext/pdf/SB01993E.pdf#navpanes=0