WASHINGTON — The front-runner in the Republican primary to become Georgia’s next governor — whose platform calls to make the Peach State “number one in the nation for deporting criminal illegal immigrants ” — failed to vet the citizenship status of workers on his own mansion, according to court documents obtained by The Post. Billionaire health care executive Rick Jackson has been involved in a workers compensation dispute after one of the laborers suffered a fall while “painting the mulch” at his palatial Cumming, Ga., estate in March 2023. According to a petition filed last month, the Georgia State Board of Workers’ Compensation erred in denying Facundo Ortega’s claim for benefits because it didn’t “consider evidence” that Jackson hired the man without checking his “work authorization.” Billionaire health care executive Rick Jackson has been involved in a workers compensation dispute after one of the laborers suffered a fall while “painting the mulch” at his palatial Cumming, Ga., estate in March 2023.…